> # moduleinvR9table.mws'' > # This program computes the quandle module invariant with R_9 > # for knots in the table up to 9 crossings in a closed braid form. > # 4-braids and larger excluded. > restart: > with(LinearAlgebra): > > # The quandle operation of R_9 is defined: > g:=proc(a, b) # Quandle operation for R_9 > 2*b - a mod 9 : end: > > # Defining matrices of action, > # 1=(29)(38)(47)(56), 2=(13)(49)(58)(67), 3=(15)(24)(69)(78), 4=(17)(26)(35)(89), > # 5=(19)(37)(28)(46), 6=(12)(39)(48)(57), 7=(14)(23)(59)(68), 8=(16)(25)(34)(79), > # 9=0=(18)(27)(36)(45). > # Here, 0 is regarded as 3 in permutation group. > M[1]:= > <<1,0,0,0,0,0,0,0,0> > |<0,0,0,0,0,0,0,0,1> > |<0,0,0,0,0,0,0,1,0> > |<0,0,0,0,0,0,1,0,0> > |<0,0,0,0,0,1,0,0,0> > |<0,0,0,0,1,0,0,0,0> > |<0,0,0,1,0,0,0,0,0> > |<0,0,1,0,0,0,0,0,0> > |<0,1,0,0,0,0,0,0,0>>: > M[2]:= > <<0,0,1,0,0,0,0,0,0> > |<0,1,0,0,0,0,0,0,0> > |<1,0,0,0,0,0,0,0,0> > |<0,0,0,0,0,0,0,0,1> > |<0,0,0,0,0,0,0,1,0> > |<0,0,0,0,0,0,1,0,0> > |<0,0,0,0,0,1,0,0,0> > |<0,0,0,0,1,0,0,0,0> > |<0,0,0,1,0,0,0,0,0>>: > M[3]:= > <<0,0,0,0,1,0,0,0,0> > |<0,0,0,1,0,0,0,0,0> > |<0,0,1,0,0,0,0,0,0> > |<0,1,0,0,0,0,0,0,0> > |<1,0,0,0,0,0,0,0,0> > |<0,0,0,0,0,0,0,0,1> > |<0,0,0,0,0,0,0,1,0> > |<0,0,0,0,0,0,1,0,0> > |<0,0,0,0,0,1,0,0,0>>: > M[4]:= > <<0,0,0,0,0,0,1,0,0> > |<0,0,0,0,0,1,0,0,0> > |<0,0,0,0,1,0,0,0,0> > |<0,0,0,1,0,0,0,0,0> > |<0,0,1,0,0,0,0,0,0> > |<0,1,0,0,0,0,0,0,0> > |<1,0,0,0,0,0,0,0,0> > |<0,0,0,0,0,0,0,0,1> > |<0,0,0,0,0,0,0,1,0>>: > M[5]:= > <<0,0,0,0,0,0,0,0,1> > |<0,0,0,0,0,0,0,1,0> > |<0,0,0,0,0,0,1,0,0> > |<0,0,0,0,0,1,0,0,0> > |<0,0,0,0,1,0,0,0,0> > |<0,0,0,1,0,0,0,0,0> > |<0,0,1,0,0,0,0,0,0> > |<0,1,0,0,0,0,0,0,0> > |<1,0,0,0,0,0,0,0,0>>: > M[6]:= > <<0,1,0,0,0,0,0,0,0> > |<1,0,0,0,0,0,0,0,0> > |<0,0,0,0,0,0,0,0,1> > |<0,0,0,0,0,0,0,1,0> > |<0,0,0,0,0,0,1,0,0> > |<0,0,0,0,0,1,0,0,0> > |<0,0,0,0,1,0,0,0,0> > |<0,0,0,1,0,0,0,0,0> > |<0,0,1,0,0,0,0,0,0>>: > M[7]:= > <<0,0,0,1,0,0,0,0,0> > |<0,0,1,0,0,0,0,0,0> > |<0,1,0,0,0,0,0,0,0> > |<1,0,0,0,0,0,0,0,0> > |<0,0,0,0,0,0,0,0,1> > |<0,0,0,0,0,0,0,1,0> > |<0,0,0,0,0,0,1,0,0> > |<0,0,0,0,0,1,0,0,0> > |<0,0,0,0,1,0,0,0,0>>: > M[8]:= > <<0,0,0,0,0,1,0,0,0> > |<0,0,0,0,1,0,0,0,0> > |<0,0,0,1,0,0,0,0,0> > |<0,0,1,0,0,0,0,0,0> > |<0,1,0,0,0,0,0,0,0> > |<1,0,0,0,0,0,0,0,0> > |<0,0,0,0,0,0,0,0,1> > |<0,0,0,0,0,0,0,1,0> > |<0,0,0,0,0,0,1,0,0>>: > M[0]:= > <<0,0,0,0,0,0,0,1,0> > |<0,0,0,0,0,0,1,0,0> > |<0,0,0,0,0,1,0,0,0> > |<0,0,0,0,1,0,0,0,0> > |<0,0,0,1,0,0,0,0,0> > |<0,0,1,0,0,0,0,0,0> > |<0,1,0,0,0,0,0,0,0> > |<1,0,0,0,0,0,0,0,0> > |<0,0,0,0,0,0,0,0,1>>: > ID:= > <<1,0,0,0,0,0,0,0,0> > |<0,1,0,0,0,0,0,0,0> > |<0,0,1,0,0,0,0,0,0> > |<0,0,0,1,0,0,0,0,0> > |<0,0,0,0,1,0,0,0,0> > |<0,0,0,0,0,1,0,0,0> > |<0,0,0,0,0,0,1,0,0> > |<0,0,0,0,0,0,0,1,0> > |<0,0,0,0,0,0,0,0,1>>: > > # The dynamical cocycle matrices are defined below. > # The goal is to define a 18X18 matrix DM[x,y] for any x,y in R_9, > # such that DM[x,y] acts from the left on colum color vectors in > # Z^9 X Z^9, when the bottom colors at a braid generator > # is (x, y). > DM:=array(0..8,0..8): > DM0:=array(0..8,0..8): > DM1:=array(0..8,0..8): > > # DM[x,y] acted on (a, b) gives (b, y.a + (ID - x*y).b), > # where $\eta_{x,y}=y$ and $\tau_{x,y}=1-x*y$, > # so first we put the ID matrix at (1,2)-block to obtain DM0[x,y]: > for k0 from 0 to 8 do > for k1 from 0 to 8 do > DM0[k0,k1]:=linalg[copyinto](ID, Matrix(18,18), 1,10): > od: > od: > > > # Then we put M[y] at (2,1)-block to obtain DM1[x,y]: > for k0 from 0 to 8 do > for k1 from 0 to 8 do > DM1[k0,k1]:=linalg[copyinto](M[k1], DM0[k0,k1], 10,1): > od: > od: > > # Finally we put (ID - M[x*y]) at (2,2)-block. > for k0 from 0 to 8 do > for k1 from 0 to 8 do > DM[k0,k1]:=linalg[copyinto](evalm(ID - M[g(k0,k1)]), DM1[k0,k1], 10,10): > od: > od: > > # Braid words of the knot table, brind is the braid index. > # 9-colorable ones picked, and renumbered for automated computation. > #bw[1]:= [1,1,1]: brind[1]:=2: > #bw[2]:= [1,-2,1,-2]: brind[2]:=3: > #bw[3]:= [1,1,1,1,1]: brind[3]:=2: > #bw[4]:= [1,1,2,2,-1,2]: brind[4]:=3: > #bw[5]:= [-1,2,-1,3,-2,3,2]: brind[5]:=4:#9-col but exc. > #bw[6]:= [-1,2,-1,2,2,2]: brind[6]:=3: > #bw[7]:= [-1,2,2,-1,-1,2]: brind[7]:=3: > #bw[8]:= [1,1,1,1,1,1,1]: brind[8]:=2: > #bw[9]:= [-1,3,3,3,2,1,1,-3,2]: brind[9]:=4: > #bw[10]:= [1,1,2,-1,2,2,2,2]: brind[10]:=3: > #bw[11]:= [1,1,2,3,3,-1,2,-3,2]: brind[11]:=4: > #bw[12]:= [1,1,1,1,2,-1,2,2]: brind[12]:=3: > #bw[13]:= [1,-2,-1,-1,3,2,2,2,3]: brind[13]:=4: > #bw[14]:= [1,-3,2,-3,2,-1,2,-3,2]: brind[14]:=4: > #bw[15]:= [-1,2,3,-2,-1,4,4,3,2,-4]: brind[15]:=5: > #bw[16]:= [-1,2,2,2,2,2,-1,2]: brind[16]:=3: > #bw[17]:= [-1,-1,-2,1,4,4,3,-4,-2,3]: brind[17]:=5: > #bw[18]:= [1,1,1,3,-2,-3,-3,1,-2]: brind[18]:=4: > #bw[19]:= [1,1,1,-2,1,1,1,-2]: brind[19]:=3: > #bw[20]:= [-1,2,-1,-3,2,2,2,3,3]: brind[20]:=4: > #bw[21]:= [1,1,1,1,-2,-2,1,-2]: brind[21]:=3: > #bw[22]:= [-1,2,1,1,-3,2,2,-3,-3]: brind[22]:=4: > #bw[23]:= [-1,2,-1,-1,-1,2,2,2]: brind[23]:=3: > #bw[24]:= [-1,2,2,-1,-1,2,2,2]: brind[24]:=3: > #bw[25]:= [-1,2,2,-3,2,3,3,-1,2]: brind[25]:=4: > #bw[26]:= [1,-2,3,-4,3,-4,2,1,-3,-2]: brind[26]:=5: > #bw[27]:= [1,1,2,-3,2,-1,-3,-3,2]: brind[27]:=4: > #bw[28]:= [1,1,2,2,-1,-3,2,-3,2]: brind[28]:=4: > #bw[29]:= [1,1,-2,1,3,3,2,2,3]: brind[29]:=4: > #bw[30]:= [1,1,-2,1,1,-2,1,-2]: brind[30]:=3: > #bw[31]:= [-1,2,-1,2,2,-1,-1,2]: brind[31]:=3: > #bw[32] > bw[1]:= [1,-2,1,-2,1,-2,1,-2]: brind[1]:=3: > #bw[33]:= [1,2,1,2,1,2,2,1]: brind[33]:=3: > #bw[34] > bw[2]:= [1,1,1,2,-1,-1,-1,2]: brind[2]:=3: > #bw[35]:= [1,-2,-2,1,1,2,2,2]: brind[35]:=3: > #bw[36] > bw[3]:= [1,1,1,1,1,1,1,1,1]: brind[3]:=2: > #bw[37]:= [1,2,3,4,4,4,3,-4,2,1,-3,-2]: brind[37]:=5: > #bw[38]:= [1,-2,1,1,1,1,1,1,2,2]: brind[38]:=3: > #bw[39]:= [-1,3,2,1,1,2,3,3,3,3,-2]: brind[39]:=4: > #bw[40]:= [1,1,2,-1,3,-2,3,4,4,3,-4,2]: brind[40]:=5: > #bw[41] > bw[4]:= [1,1,2,2,1,1,1,1,1,-2]: brind[4]:=3: > #bw[42]:= [1,1,1,2,3,3,-1,2,2,2,-3]: brind[42]:=4: > #bw[43]:= [1,-2,3,-1,-1,-4,3,-2,3,3,4,3]: brind[43]:=5: > #bw[44]:= [1,1,1,-2,1,1,1,1,2,2]: brind[44]:=3: > #bw[45]:= [-1,2,1,1,2,2,2,-3,2,3,3]: brind[45]:=4: > #bw[46]:= [-1,2,-3,2,-1,2,2,2,2,3,2]: brind[46]:=4: > #bw[47]:= [1,-2,-1,-1,3,2,2,2,4,4,3,-4]: brind[47]:=5: > #bw[48]:= [1,1,2,-3,2,-1,3,3,2,2,2]: brind[48]:=4: > #bw[49]:= [1,4,4,-3,2,-3,2,-3,-1,-4,2,2,3,-2]: brind[49]:=5: > #bw[50]:= [1,-2,1,3,-2,4,-3,4,4,3]: brind[50]:=5: > #bw[51]:= [1,1,-2,1,1,1,2,2,2,2]: brind[51]:=3: > #bw[52]:= [1,1,1,3,-2,1,-2,-3,-2,1,-2]: brind[52]:=4: > #bw[53]:= [1,1,-3,2,-1,2,2,3,3,2,2]: brind[53]:=4: > #bw[54]:= [1,1,2,-1,-3,-4,-3,2,-3,2,4,-3]: brind[54]:=5: > #bw[55]:= [1,2,2,-3,2,-1,2,-3,2,2,2]: brind[55]:=4: > #bw[56]:= [-1,-1,3,-4,3,-2,1,3,4,4,2,2]: brind[56]:=5: > #bw[57]:= [1,-2,3,3,3,-2,3,-1,-2,3,-2]: brind[57]:=4: > #bw[58]:= [1,-2,1,1,2,3,3,3,2,-3,2]: brind[58]:=4:#9-col but exc. > #bw[59]:= [1,3,3,-2,1,3,-2,-2,-2]: brind[59]:=4:#9-col but exc. > #bw[60]:= [-1,2,-1,-4,-3,2,4,4,3,4,4,2,2,-3]: brind[60]:=5: > #bw[61]:= [-1,2,2,2,3,2,-1,2,-1,-3,2]: brind[61]:=4: > #bw[62]:= [-1,2,-1,-1,-3,2,-1,2,2,3,2]: brind[62]:=4: > #bw[63]:= [1,1,3,3,-2,-2,1,3,-2]: brind[63]:=4: > #bw[64]:= [-1,2,-3,2,-1,2,-3,2,2]: brind[64]:=4: > #bw[65]:= [1,-3,-3,2,-3,-1,2,1,1,-3,2]: brind[65]:=4: > #bw[66]:= [-1,2,2,-3,2,2,-1,2,3,-1,2]: brind[66]:=4: > #bw[67]:= [-1,2,3,-1,2,-1,3,3,2,-3,2]: brind[67]:=4: > #bw[68]:= [-1,-1,-1,2,-1,2,2,3,1,-2,3]: brind[68]:=4: > #bw[69]:= [1,-2,3,-2,1,-2,3,1,-2]: brind[69]:=4: > #bw[70]:= [1,3,3,-4,-2,1,2,3,3,2,-3,4,-3,2]: brind[70]:=5:#9-col but exc. > #bw[71]:= [-1,2,2,2,-3,2,3,3,-1,2,3]: brind[71]:=4: > #bw[72]:= [1,-2,3,-2,3,-1,4,-3,-2,4,3,-2]: brind[72]:=5:#9-col but exc. > #bw[73]:= [1,1,2,3,3,2,2,-1,2,-3,2]: brind[73]:=4: > #bw[74]:= [-1,-3,2,4,3,3,-1,2,2,3,4,-2]: brind[74]:=5: > #bw[75]:= [1,3,-2,3,1,-2,1,3,-2]: brind[75]:=4: > #bw[76]:= [-1,2,2,-4,3,-4,-2,1,-3,2,3,-4,3,2]: brind[76]:=5: > #bw[77]:= [1,1,1,3,-2,3,-1,-1,-2]: brind[77]:=4: > #bw[78]:= [1,2,1,1,2,2,3,-2,1,-2,-3]: brind[78]:=4: > #bw[79]:= [-1,2,-1,3,-2,3,2,2,-3]: brind[79]:=4: > #bw[80]:= [1,-2,1,3,2,2,2,3,-2]: brind[80]:=4: > #bw[81]:= [1,3,2,-1,-3,2,1,3,-2]: brind[81]:=4:#9-col but exc. > #bw[82]:= [-1,2,3,-1,2,-1,2,3,2]: brind[82]:=4:#9-col but exc. > #bw[83]:= [1,1,-2,3,2,2,-1,-3,2,-3,2]: brind[83]:=4:#9-col but exc. > #bw[84]:= [1,1,2,2,3,2,-1,2,2,3,-2]: brind[84]:=4:#9-col but exc. > > # Computing the module invariant one by one: > for KT from 1 to 4 do > # KT represents the number of a given knot in the table above. > > print(Knot, KT); > > # The following makes bigger dynamical cocycle matrices, > # depending on the index of a given braid, for each generator and > # each bottom color vectors. > BigID:=Matrix(1..(9*brind[KT]),1..(9*brind[KT]),shape=identity): > # This is the identity matrix of the size > # Z^9(braid index) the braid index of the given braid. > > for jj0 from 1 to brind[KT]-1 do > for jj1 from 0 to 8 do > for jj2 from 0 to 8 do > ColoredBurau[jj0,jj1,jj2]:=convert( > # converting ``matrix'' of linalg to ``Matrix'' of LinearAlgebra. > linalg[copyinto](DM[jj1,jj2], BigID, (9*jj0 -8),(9*jj0 -8)), > Matrix): > od: > od: > od: > # This is the cocycle matrix put at the braid generator's place. > # If the braid generator is $\sigma_{jj0}$, with bottom color vector > # $(jj1, jj2) \in (R_9)^2$, then ColoredBurau[jj0,jj1,jj2] acts. > > for jj00 from 1 to brind[KT]-1 do > for jj10 from 0 to 8 do > for jj20 from 0 to 8 do > ColoredBurau[-jj00,jj10,jj20]:=convert( > MatrixInverse(ColoredBurau[jj00,g(jj20,jj10),jj10]), > Matrix): > od: > od: > od: > # This is the inverse, corresponding to $\sigma_{jj0}^{-1}$ > # with the bottom colors $(jj10, jj20) \in (R_9)^2$. > > # Color vectors. > for jj3 from 1 to (nops(bw[KT])+1) do > Color[jj3]:=array(1..brind[KT]): > od: > > # Producing all color vectors. > num:=9^(brind[KT]) : > for indx from 0 to (num-1) do # One color at a time. > > for jj5 from 1 to brind[KT] do > Color[1][jj5]:=iquo(indx,9^(jj5-1)) mod 9: > od: > > # Defining Burau rep for R_9, acting from the right to row vectors. > #Burau:=linalg[matrix](2,2,[0,-1,1,2]): > #Burinv:=linalg[matrix](2,2,[2,1,-1,0]): > #### Note: I am switching Burau and Burinv, since the negative crossing > #### is the positive generator. And the matrices act from left to row vecs > #### from top to bottom. This convention is different from ColoredBurau. > Burau:=linalg[matrix](2,2,[2,1,-1,0]): > Burinv:=linalg[matrix](2,2,[0,-1,1,2]): > > for j0 from 1 to brind[KT]-1 do # Copying the Burau matrix into bigger ones. > B[j0]:=array(1..brind[KT],1..brind[KT]): > B[-j0]:=array(1..brind[KT],1..brind[KT]): > od; > ID:=Matrix(1..brind[KT],1..brind[KT],shape=identity); > for j1 from 1 to brind[KT]-1 do > for j2 from 1 to brind[KT] do > for j3 from 1 to brind[KT] do > B[j1][j2,j3]:=linalg[copyinto](Burau, ID, j1,j1)[j2,j3]: > B[-j1][j2,j3]:=linalg[copyinto](Burinv, ID, j1,j1)[j2,j3]: > od: od: od: > > # Computing all color vectors. > for jj6 from 1 to nops(bw[KT]) do > Newcolorvec[jj6]:=evalm(Color[jj6] &* B[bw[KT][jj6]]): > for jj8 from 1 to brind[KT] do > Color[jj6+1][jj8]:=map( z -> z mod 9, Newcolorvec[jj6][jj8]): > od: > od: > > # Finding if the colors match. > ColorDiff0:=evalm(Color[1] - Color[nops(bw[KT])+1]): > ColDiffMatch0:=sum(abs(ColorDiff0[jj]), jj=1..brind[KT]): > # This is zero iff the top color vec matches the bottom. > > if (ColDiffMatch0=0) then > > # Computing the presentation matrix. > # Note that we have to use the colors assigned to the bottom arcs. > PR[1]:=ColoredBurau[bw[KT][1], Color[2][abs(bw[KT][1])], Color[2][abs(bw[KT][1])+1]]: > > for jj7 from 1 to nops(bw[KT])-1 do > PR[jj7+1]:=MatrixMatrixMultiply(PR[jj7], > ColoredBurau[bw[KT][jj7+1], Color[jj7+2][abs(bw[KT][jj7+1])], Color[jj7+2][abs(bw[KT][jj7+1])+1]]): > od: > > PRM:=evalm(PR[nops(bw[KT])] - BigID): > > PRMatrix:=convert(PRM, Matrix): > > PRMSmith:=SmithForm(PRMatrix): > > PRMdiag:=[]: > for jj8 from 1 to 9*(brind[KT]) do > PRMdiag:=[ op(PRMdiag), PRMSmith[jj8,jj8] ]: > od: > > print(TopColor, Color[1], TorsionCoefficients, PRMdiag); > > else > end if: > > od: # Closing each color. > od: # Closing KT. > > Knot, 1 TopColor, [0, 0, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 0, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 0, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 3, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 3, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 3, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 6, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 6, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 6, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 1, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 1, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 1, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 4, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 4, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 4, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 7, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 7, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 7, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 2, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 2, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 2, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 5, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 5, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 5, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 8, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 8, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 8, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 0, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 0, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 0, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 3, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 3, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 3, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 6, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 6, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 6, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 1, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 1, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 1, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 4, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 4, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 4, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 7, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 7, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 7, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 2, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 2, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 2, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 5, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 5, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 5, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 8, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 8, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 8, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 0, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 0, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 0, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 3, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 3, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 3, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 6, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 6, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 6, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 1, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 1, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 1, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 4, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 4, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 4, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 7, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 7, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 7, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 2, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 2, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 2, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 5, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 5, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 5, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 8, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 8, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 8, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0] Knot, 2 TopColor, [0, 0, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 0, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 0, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 3, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 3, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 3, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 6, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 6, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 6, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 1, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 1, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 1, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 4, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 4, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 4, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 7, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 7, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 7, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 2, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 2, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 2, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 5, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 5, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 5, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 8, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 8, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 8, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 0, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 0, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 0, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 3, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 3, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 3, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 6, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 6, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 6, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 1, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 1, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 1, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 4, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 4, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 4, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 7, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 7, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 7, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 2, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 2, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 2, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 5, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 5, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 5, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 8, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 8, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 8, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 0, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 0, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 0, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 3, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 3, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 3, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 6, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 6, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 6, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 1, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 1, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 1, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 4, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 4, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 4, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 7, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 7, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 7, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 2, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 2, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 2, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 5, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 5, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 5, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 8, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 8, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 8, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] Knot, 3 TopColor, [0, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0] Knot, 4 TopColor, [0, 0, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 27, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 1, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 2, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 3, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 4, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 5, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 6, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 7, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 8, 0], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 0, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 1, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 27, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 2, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 3, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 4, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 5, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 6, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 7, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 8, 1], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 0, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 1, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 2, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 27, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 3, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 4, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 5, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 6, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 7, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 8, 2], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 0, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 1, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 2, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 3, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 27, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 4, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 5, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 6, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 7, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 8, 3], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 0, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 1, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 2, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 3, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 4, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 27, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 5, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 6, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 7, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 8, 4], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 0, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 1, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 2, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 3, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 4, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 5, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 27, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 6, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 7, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 8, 5], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 0, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 1, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 2, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 3, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 4, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 5, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [6, 6, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 27, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [0, 7, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [3, 8, 6], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 0, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 1, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 2, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 3, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 4, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 5, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [4, 6, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [7, 7, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 27, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [1, 8, 7], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 0, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 1, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 2, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 3, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 4, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 5, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [2, 6, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [5, 7, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] TopColor, [8, 8, 8], TorsionCoefficients, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 27, 27, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0]