##
##
##                    mega.mpl
##               simulates the moves of the megaminx
##
##                                         David Joyner, 1996-7
###########################################################

A0:=array([
 [1,1,1,1,1,1,1,1,1,1,1],
 [2,2,2,2,2,2,2,2,2,2,2],
 [3,3,3,3,3,3,3,3,3,3,3],
 [4,4,4,4,4,4,4,4,4,4,4],
 [5,5,5,5,5,5,5,5,5,5,5],
 [6,6,6,6,6,6,6,6,6,6,6],
 [7,7,7,7,7,7,7,7,7,7,7],
 [8,8,8,8,8,8,8,8,8,8,8],
 [9,9,9,9,9,9,9,9,9,9,9],
 [10,10,10,10,10,10,10,10,10,10,10],
 [11,11,11,11,11,11,11,11,11,11,11],
 [12,12,12,12,12,12,12,12,12,12,12]]):

# For reference:
#   A[1]=f1=up,A[2]=f2,A[3]=f3,A[4]=f4,A[5]=f5,A[6]=f6,
#   A[7]=f7,A[8]=f8,A[9]=f9,A[10]=f10,A[11]=f11,A[12]=f12.

# For reference:
position_matrix:=array([
 [1,2,3,4,5,6,7,8,9,10,11],
 [12,13,14,15,16,17,18,19,20,21,22],
 [23,24,25,26,27,28,29,30,31,32,33],
 [34,35,36,37,38,39,40,41,42,43,44],
 [45,46,47,48,49,50,51,52,53,54,55],
 [56,57,58,59,60,61,62,63,64,65,66],
 [67,68,69,70,71,72,73,74,75,76,77],
 [78,79,80,81,82,83,84,85,86,87,88],
 [89,90,91,92,93,94,95,96,97,98,99],
 [100,101,102,103,104,105,106,107,108,109,110],
 [111,112,113,114,115,116,117,118,119,120,121],
 [122,123,124,125,126,127,128,129,130,131,132]]):

color7:=white:
color1 := red:
color2 := blue:
color3 := coral:
macro(mycolor1=COLOR(RGB, .6607, .3372, .7607)):
color4 := mycolor1:
color5 := green:
color6 := yellow:
color0 := turquoise:
color8 := pink:
macro(mycolor2=COLOR(RGB, .2607, .9372, .8607)):
color9 := mycolor2:
color10 := aquamarine:
color11 := cyan:
color12 := magenta:

A0:=array([
[1,1,1,1,1,1,1,1,1,1,1],
[2,2,2,2,2,2,2,2,2,2,2],
[3,3,3,3,3,3,3,3,3,3,3],
[4,4,4,4,4,4,4,4,4,4,4],
[5,5,5,5,5,5,5,5,5,5,5],
[6,6,6,6,6,6,6,6,6,6,6],
[7,7,7,7,7,7,7,7,7,7,7],
[8,8,8,8,8,8,8,8,8,8,8],
[9,9,9,9,9,9,9,9,9,9,9],
[10,10,10,10,10,10,10,10,10,10,10],
[11,11,11,11,11,11,11,11,11,11,11],
[12,12,12,12,12,12,12,12,12,12,12]]):

phi := 1/2*5^(1/2)+1/2:
pt:=(a,b,t)->expand((b-a)*t+a):

P1:=[1,0,phi]: P2:=[1,0,-phi]: P3:=[0,phi,1]: P4:=[-1,0,-phi]:
P5:=[-1,0,phi]: P6:=[phi,1,0]: P7:=[-phi,1,0]: P8:=[-phi,-1,0]:
P9:=[0,phi,-1]: P10:=[0,-phi,-1]: P11:=[0,-phi,1]: P12:=[phi,-1,0]:

Q1:=(P1+P3+P6)/3: Q2:=(P1+P5+P11)/3: Q3:=(P1+P11+P12)/3: 
Q4:=(P1+P12+P6)/3:
 q_1_3_6:=(P1+P3+P6)/3: q_1_5_11:=(P1+P5+P11)/3: q_1_11_12:=(P1+P11+P12)/3: 
 q_1_6_12:=(P1+P12+P6)/3:
Q5:=(P9+P2+P6)/3: Q6:=(P9+P3+P6)/3: Q7:=(P9+P3+P7)/3: 
Q8:=(P5+P8+P7)/3:
 q_2_6_9:=(P9+P2+P6)/3: q_3_6_9:=(P9+P3+P6)/3: 
 q_3_7_9:=(P9+P3+P7)/3: q_5_7_8:=(P5+P8+P7)/3:
 q_10_11_12:=(P12+P11+P10)/3: 
Q9:=(P12+P11+P10)/3: Q10:=(P9+P2+P4)/3: Q11:=(P2+P12+P6)/3: 
Q12:=(P2+P12+P10)/3: Q13:=(P2+P10+P4)/3:
 q_2_4_9:=(P9+P2+P4)/3: q_2_6_12:=(P2+P12+P6)/3: q_2_10_12:=(P2+P12+P10)/3:
 q_2_4_10:=(P2+P10+P4)/3:
Q15:=(P1+P3+P5)/3: Q14:=(P7+P3+P5)/3: Q16:=(P4+P7+P9)/3: 
Q17:=(P7+P8+P4)/3:
 q_1_3_5:=(P1+P3+P5)/3: q_3_5_7:=(P7+P3+P5)/3: 
 q_4_7_9:=(P4+P7+P9)/3: q_4_7_8:=(P7+P8+P4)/3:
Q18:=(P10+P8+P11)/3: Q19:=(P4+P8+P10)/3: Q20:=(P5+P11+P8)/3:
 q_8_10_11:=(P10+P8+P11)/3: q_4_8_10:=(P4+P8+P10)/3: 
 q_5_8_11:=(P5+P11+P8)/3:

Q1617a:=(2/3)*Q16+(1/3)*Q17: Q1617b:=(1/3)*Q16+(2/3)*Q17:
Q1319a:=(2/3)*Q13+(1/3)*Q19: Q1319b:=(1/3)*Q13+(2/3)*Q19:

dodec:=proc()
local dod1,dod2,dod3,dod4,dod5,dod6,dod7,dod8,dod9,dod10,dod11,dod12;
dod.1:=polygonplot3d([q_1_3_6,q_1_3_5,q_1_5_11,q_1_11_12,q_1_6_12,q_1_3_6],
color=color1,style=patch):
dod.2:=polygonplot3d([q_2_6_12,q_2_6_9,q_2_4_9,q_2_4_10,q_2_10_12,q_2_6_12],
color=color2,style=patch):
dod.3:=polygonplot3d([q_1_3_6,q_1_3_5,q_3_5_7,q_3_7_9,q_3_6_9,q_1_3_6],
color=color3,style=patch):
dod.4:=polygonplot3d([q_4_7_8,q_4_7_9,q_2_4_9,q_2_4_10,q_4_8_10,q_4_7_8],
color=color4,style=patch):
dod.5:=polygonplot3d([q_5_8_11,q_5_7_8,q_3_5_7,q_1_3_5,q_1_5_11,q_5_8_11],
color=color5,style=patch):
dod.6:=polygonplot3d([q_1_3_6,q_3_6_9,q_2_6_9,q_2_6_12,q_1_6_12,q_1_3_6],
color=color6,style=patch):
dod.7:=polygonplot3d([q_5_7_8,q_4_7_8,q_4_7_9,q_3_7_9,q_3_5_7,q_5_7_8],
color=color0,style=patch):
dod.8:=polygonplot3d([q_5_8_11,q_5_7_8,q_4_7_8,q_4_8_10,q_8_10_11,q_5_8_11],
color=color8,style=patch):
dod.9:=polygonplot3d([q_4_7_9,q_2_4_9,q_2_6_9,q_3_6_9,q_3_7_9,q_4_7_9],
color=color9,style=PATCH):
dod.10:=polygonplot3d([q_2_4_10,q_2_10_12,q_10_11_12,q_8_10_11,q_4_8_10,q_2_4_10],
color=color10,style=patch):
dod.11:=polygonplot3d([q_10_11_12,q_8_10_11,q_5_8_11,q_1_5_11,q_1_11_12,q_10_11_12],
color=color11,style=patch):
dod.12:=polygonplot3d([q_1_11_12,q_10_11_12,q_2_10_12,q_2_6_12,q_1_6_12,q_1_11_12],
color=color12,style=patch):
display3d([seq(dod.i,i=1..12)],title=`full dodecahedron`);
end:

faces:=proc(A::array)
##
## A is the 12x11 array of colors
## optional argument: [theta,phi] = orientation
##
local face1,face2,face3,face4,face5,face6,face7,face8,face9,
face10,face11,face12,theta,phi;
if nargs=2 then theta:=args[2][1]; phi:=args[2][2]; 
  else theta:=45; phi:=85; 
fi;
face1:=facets(q_1_3_6,q_1_3_5,q_1_5_11,q_1_11_12,q_1_6_12,linalg[row](A,1)):
face2:=facets(q_1_6_12,q_1_11_12,q_10_11_12,q_2_10_12,q_2_6_12,linalg[row](A,2));
face3:=facets(q_1_11_12,q_1_5_11,q_5_8_11,q_8_10_11,q_10_11_12,linalg[row](A,3));
face10:=facets(q_5_7_8,q_3_5_7,q_3_7_9,q_4_7_9,q_4_7_8,linalg[row](A,10));
face5:=facets(q_1_3_5,q_1_3_6,q_3_6_9,q_3_7_9,q_3_5_7,linalg[row](A,5)):
face12:=facets(q_4_7_9,q_2_4_9,q_2_4_10,q_4_8_10,q_4_7_8,linalg[row](A,12));
face4:=facets(q_1_5_11,q_1_3_5,q_3_5_7,q_5_7_8,q_5_8_11,linalg[row](A,4));
face6:=facets(q_1_3_6,q_1_6_12,q_2_6_12,q_2_6_9,q_3_6_9,linalg[row](A,6));
face9:=facets(q_8_10_11,q_5_8_11,q_5_7_8,q_4_7_8,q_4_8_10,linalg[row](A,9));
face11:=facets(q_3_7_9,q_3_6_9,q_2_6_9,q_2_4_9,q_4_7_9,linalg[row](A,11));
face8:=facets(q_2_10_12,q_10_11_12,q_8_10_11,q_4_8_10,q_2_4_10,linalg[row](A,8));
face7:=facets(q_2_6_12,q_2_10_12,q_2_4_10,q_2_4_9,q_2_6_9,linalg[row](A,7)):
display3d([face1,face2,face3,face4,face5,face6,face7,face8,
 face9,face10,face11,face12],orientation=[theta,phi]);
end:

facets:=proc(P5::list,P4::list,P3::list,P2::list,P1::list,A::array)
##
## P1,...,P5 are the vertices of the pentagonal face
## A is the array of 11 colors (clockwise then center)
##
local facet1,facet2,facet3,facet4,facet5,facet6,facet7,facet8,facet9,
facet10,facet11,facet12;

facet1:=polygonplot3d([P1,pt(P1,P2,1/3),
 (0.74)*P1+(.26)*(P3+P4)/2,pt(P1,P5,1/3),P1],
 color=color.(A[1]),style=patch): #corner
facet3:=polygonplot3d([P2,pt(P2,P3,1/3),
 (0.74)*P2+(.26)*(P4+P5)/2,pt(P1,P2,2/3),P2],
 color=color.(A[3]),style=patch): #corner
facet5:=polygonplot3d([P3,pt(P3,P4,1/3),
 (0.74)*P3+(.26)*(P1+P5)/2,pt(P3,P2,1/3),P3],
 color=color.(A[5]),style=patch): #corner
facet7:=polygonplot3d([P4,pt(P5,P4,2/3),
 (0.74)*P4+(.26)*(P1+P2)/2,pt(P4,P3,1/3),P4],
 color=color.(A[7]),style=patch): #corner
facet9:=polygonplot3d([P5,pt(P5,P1,1/3),
 (0.74)*P5+(.26)*(P2+P3)/2,pt(P4,P5,2/3),P5],
 color=color.(A[9]),style=patch): #corner

facet11:=polygonplot3d([(0.74)*P1+(.26)*(P3+P4)/2,
(0.74)*P2+(.26)*(P4+P5)/2,
(0.74)*P2+(.26)*(P4+P5)/2,
(0.74)*P3+(.26)*(P1+P5)/2,
 (0.74)*P4+(.26)*(P1+P2)/2,
(0.74)*P5+(.26)*(P2+P3)/2,
(0.74)*P1+(.26)*(P3+P4)/2], color=color.(A[11]),style=patch): #center

facet10:=polygonplot3d([pt(P5,P1,2/3),pt(P5,P1,1/3),
(0.74)*P5+(.26)*(P2+P3)/2,(0.74)*P1+(.26)*(P3+P4)/2,
pt(P5,P1,2/3)], color=color.(A[10]),style=patch): #edge
facet2:=polygonplot3d([pt(P2,P1,2/3),pt(P2,P1,1/3),
(0.74)*P2+(.26)*(P4+P5)/2,(0.74)*P1+(.26)*(P3+P4)/2,
pt(P2,P1,2/3)], color=color.(A[2]),style=patch): #edge
facet8:=polygonplot3d([pt(P5,P4,1/3),pt(P4,P5,1/3),
(0.74)*P4+(.26)*(P2+P1)/2,(0.74)*P5+(.26)*(P2+P3)/2,
pt(P4,P5,2/3)], color=color.(A[8]),style=patch): #edge
facet6:=polygonplot3d([pt(P3,P4,1/3),pt(P4,P3,1/3),
(0.74)*P4+(.26)*(P2+P1)/2,(0.74)*P3+(.26)*(P1+P5)/2,
pt(P3,P4,1/3)], color=color.(A[6]),style=patch): #edge
facet4:=polygonplot3d([pt(P2,P3,1/3),pt(P3,P2,1/3),
(0.74)*P3+(.26)*(P5+P1)/2,(0.74)*P2+(.26)*(P4+P5)/2,
pt(P2,P3,1/3)], color=color.(A[4]),style=patch): #edge
display3d([facet1,facet3,facet4,facet5,facet6,facet7,facet8,
 facet9,facet10,facet11,facet2]);
end:

list2array:=proc(n::integer)
##
## converts position number 1..132 to 11x12 array index
##
if 0<n and n<12 then RETURN([1,n]); fi;
if 11<n and n<23 then RETURN([2,n-11]); fi;
if 22<n and n<34 then RETURN([3,n-22]); fi;
if 33<n and n<45 then RETURN([4,n-33]); fi;
if 44<n and n<56 then RETURN([5,n-44]); fi;
if 55<n and n<67 then RETURN([6,n-55]); fi;
if 66<n and n<78 then RETURN([7,n-66]); fi;
if 77<n and n<89 then RETURN([8,n-77]); fi;
if 88<n and n<100 then RETURN([9,n-88]); fi;
if 99<n and n<111 then RETURN([10,n-99]); fi;
if 110<n and n<122 then RETURN([11,n-110]); fi;
if 121<n and n<133 then RETURN([12,n-121]); fi;
end:

move_f1:=proc(A::array)
##
## A is the 11x12 array of colors
## optional argument: [theta,phi] = orientation
##
## rotates f1 facet by 2Pi/5 radians clockwise
## megaminx with color array A
## RETURNs new color array AA
##
local AA,A1,i,j,j1,j2,k1,k2,templist;
templist.1:=[1,3,5,7,9,1];
templist.2:=[2,4,6,8,10,2];
templist.3:=[18,29,40,51,62,18];
templist.4:=[19,30,41,52,63,19];
templist.5:=[20,31,42,53,64,20];
for i from 1 to 12 do
 for j from 1 to 11 do
 AA[i,j]:=A[i,j];
 od;
od;
AA[list2array(62)[1],list2array(62)[2]]:=A[list2array(18)[1],list2array(18)[2]];
AA[list2array(63)[1],list2array(63)[2]]:=A[list2array(19)[1],list2array(19)[2]];
AA[list2array(64)[1],list2array(64)[2]]:=A[list2array(20)[1],list2array(20)[2]];
AA[list2array(9)[1],list2array(9)[2]]:=A[list2array(1)[1],list2array(1)[2]];
AA[list2array(10)[1],list2array(10)[2]]:=A[list2array(2)[1],list2array(2)[2]];
for j from 1 to 5 do
 for i from 1 to nops(templist.j)-2 do
 j1:=list2array(templist.j[i])[1];
 k1:=list2array(templist.j[i])[2];
 j2:=list2array(templist.j[i+1])[1];
 k2:=list2array(templist.j[i+1])[2];
 AA[j1,k1]:=A[j2,k2];
od;
od;
A1:=array(1..12,1..11,[seq([seq(AA[j,i],i=1..11)],j=1..12)]);
RETURN(A1);
end:

move_f2:=proc(A::array)
##
## A is the 11x12 array of colors
## optional argument: [theta,phi] = orientation
##
## rotates f2 facet by 2Pi/5 radians clockwise
## megaminx with color array A
## RETURNs new color array AA
##
local AA,A1,i,j,j1,j2,k1,k2,templist;
templist.1:=[12,14,16,18,20,12];
templist.2:=[13,15,17,19,21,13];
templist.3:=[1,60,73,84,31,1];
templist.4:=[2,61,74,85,32,2];
templist.5:=[3,62,75,86,23,3];
for i from 1 to 12 do
 for j from 1 to 11 do
 AA[i,j]:=A[i,j];
 od;
od;
AA[list2array(20)[1],list2array(20)[2]]:=A[list2array(12)[1],list2array(12)[2]];
AA[list2array(21)[1],list2array(21)[2]]:=A[list2array(13)[1],list2array(13)[2]];
AA[list2array(31)[1],list2array(31)[2]]:=A[list2array(1)[1],list2array(1)[2]];
AA[list2array(32)[1],list2array(32)[2]]:=A[list2array(2)[1],list2array(2)[2]];
AA[list2array(23)[1],list2array(23)[2]]:=A[list2array(3)[1],list2array(3)[2]];
for j from 1 to 5 do
 for i from 1 to nops(templist.j)-2 do
 j1:=list2array(templist.j[i])[1];
 k1:=list2array(templist.j[i])[2];
 j2:=list2array(templist.j[i+1])[1];
 k2:=list2array(templist.j[i+1])[2];
 AA[j1,k1]:=A[j2,k2];
od;
od;
A1:=array(1..12,1..11,[seq([seq(AA[j,i],i=1..11)],j=1..12)]);
RETURN(A1);
end:

move_f3:=proc(A::array)
##
## A is the 11x12 array of colors
## optional argument: [theta,phi] = orientation
##
## rotates f3 facet by 2Pi/5 radians clockwise
## megaminx with color array A
## RETURNs new color array AA
##
local AA,A1,i,j,j1,j2,k1,k2,templist;
templist.1:=[23,25,27,29,31,23];
templist.2:=[24,26,28,30,32,24];
templist.3:=[3,16,82,95,42,3];
templist.4:=[4,17,83,96,43,4];
templist.5:=[5,18,84,97,34,5];
for i from 1 to 12 do
 for j from 1 to 11 do
 AA[i,j]:=A[i,j];
 od;
od;
AA[list2array(31)[1],list2array(31)[2]]:=A[list2array(23)[1],list2array(23)[2]];
AA[list2array(32)[1],list2array(32)[2]]:=A[list2array(24)[1],list2array(24)[2]];
AA[list2array(42)[1],list2array(42)[2]]:=A[list2array(3)[1],list2array(3)[2]];
AA[list2array(43)[1],list2array(43)[2]]:=A[list2array(4)[1],list2array(4)[2]];
AA[list2array(34)[1],list2array(34)[2]]:=A[list2array(5)[1],list2array(5)[2]];
for j from 1 to 5 do
 for i from 1 to nops(templist.j)-2 do
 j1:=list2array(templist.j[i])[1];
 k1:=list2array(templist.j[i])[2];
 j2:=list2array(templist.j[i+1])[1];
 k2:=list2array(templist.j[i+1])[2];
 AA[j1,k1]:=A[j2,k2];
od;
od;
A1:=array(1..12,1..11,[seq([seq(AA[j,i],i=1..11)],j=1..12)]);
RETURN(A1);
end:

move_f4:=proc(A::array)
##
## A is the 11x12 array of colors
## optional argument: [theta,phi] = orientation
##
## rotates f4 facet by 2Pi/5 radians clockwise
## megaminx with color array A
## RETURNs new color array AA
##
local A1,A2,A3;
A1:=evalm(move_power(F1^2,A));
A2:=evalm(move_f2(A1));
A3:=evalm(move_power(F1^(-2),A2));
RETURN(A3);
end:

move_f5:=proc(A::array)
##
## A is the 11x12 array of colors
## optional argument: [theta,phi] = orientation
##
## rotates f5 facet by 2Pi/5 radians clockwise
## megaminx with color array A
## RETURNs new color array AA
##
local A1,A2,A3;
A1:=evalm(move_power(F1^3,A));
A2:=evalm(move_f2(A1));
A3:=evalm(move_power(F1^(-3),A2));
RETURN(A3);
end:

move_f6:=proc(A::array)
##
## A is the 11x12 array of colors
## optional argument: [theta,phi] = orientation
##
## rotates f6 facet by 2Pi/5 radians clockwise
## megaminx with color array A
## RETURNs new color array AA
##
local AA,A1,i,j,j1,j2,k1,k2,templist;
templist.1:=[56,58,60,62,64,56];
templist.2:=[57,59,61,63,65,57];
templist.3:=[49,115,75,20,9,49];
templist.4:=[50,116,76,21,10,50];
templist.5:=[51,117,67,12,1,51];
for i from 1 to 12 do
 for j from 1 to 11 do
 AA[i,j]:=A[i,j];
 od;
od;
AA[list2array(64)[1],list2array(64)[2]]:=A[list2array(56)[1],list2array(56)[2]];
AA[list2array(65)[1],list2array(65)[2]]:=A[list2array(57)[1],list2array(57)[2]];
AA[list2array(9)[1],list2array(9)[2]]:=A[list2array(49)[1],list2array(49)[2]];
AA[list2array(10)[1],list2array(10)[2]]:=A[list2array(50)[1],list2array(50)[2]];
AA[list2array(1)[1],list2array(1)[2]]:=A[list2array(51)[1],list2array(51)[2]];
for j from 1 to 5 do
 for i from 1 to nops(templist.j)-2 do
 j1:=list2array(templist.j[i])[1];
 k1:=list2array(templist.j[i])[2];
 j2:=list2array(templist.j[i+1])[1];
 k2:=list2array(templist.j[i+1])[2];
 AA[j1,k1]:=A[j2,k2];
od;
od;
A1:=array(1..12,1..11,[seq([seq(AA[j,i],i=1..11)],j=1..12)]);
RETURN(A1);
end:

move_F1:=proc(A::array)
##
## A is the 11x12 array of colors
## optional argument: [theta,phi] = orientation
##
## rotates SOLID megaminx about f1 facet by 2Pi/5 radians 
## counterclockwise with color array A
## RETURNs new color array AA
##
local AA,A1,i,j,j1,j2,k1,k2,templist;
templist.1:=[1,3,5,7,9,1];
templist.2:=[2,4,6,8,10,2];
templist.3:=[18,29,40,51,62,18];
templist.4:=[19,30,41,52,63,19];
templist.5:=[20,31,42,53,64,20];
templist.6:=[22,33,44,55,66,22];
templist.7:=[21,32,43,54,65,21];
templist.8:=[12,23,34,45,56,12];
templist.9:=[13,24,35,46,57,13];
templist.10:=[14,25,36,47,58,14];
templist.11:=[15,26,37,48,59,15];
templist.12:=[16,27,38,49,60,16];
templist.13:=[17,28,39,50,61,17];
templist.14:=[77,88,99,110,121,77];
templist.15:=[67,86,97,108,119,67];
templist.16:=[68,87,98,109,120,68];
templist.17:=[69,78,89,100,111,69];
templist.18:=[70,79,90,101,112,70];
templist.19:=[71,80,91,102,113,71];
templist.20:=[72,81,92,103,114,72];
templist.21:=[73,82,93,104,115,73];
templist.22:=[74,83,94,105,116,74];
templist.23:=[75,84,95,106,117,75];
templist.24:=[76,85,96,107,118,76];
templist.25:=[130,128,126,124,122,130];
templist.26:=[131,129,127,125,123,131];
for i from 1 to 12 do
 for j from 1 to 11 do
 AA[i,j]:=A[i,j];
 od;
od;
AA[list2array(62)[1],list2array(62)[2]]:=A[list2array(18)[1],list2array(18)[2]];
AA[list2array(63)[1],list2array(63)[2]]:=A[list2array(19)[1],list2array(19)[2]];
AA[list2array(64)[1],list2array(64)[2]]:=A[list2array(20)[1],list2array(20)[2]];
AA[list2array(9)[1],list2array(9)[2]]:=A[list2array(1)[1],list2array(1)[2]];
AA[list2array(10)[1],list2array(10)[2]]:=A[list2array(2)[1],list2array(2)[2]];
AA[list2array(65)[1],list2array(65)[2]]:=A[list2array(21)[1],list2array(21)[2]];
AA[list2array(66)[1],list2array(66)[2]]:=A[list2array(22)[1],list2array(22)[2]];
AA[list2array(56)[1],list2array(56)[2]]:=A[list2array(12)[1],list2array(12)[2]];
AA[list2array(57)[1],list2array(57)[2]]:=A[list2array(13)[1],list2array(13)[2]];
AA[list2array(58)[1],list2array(58)[2]]:=A[list2array(14)[1],list2array(14)[2]];
AA[list2array(59)[1],list2array(59)[2]]:=A[list2array(15)[1],list2array(15)[2]];
AA[list2array(60)[1],list2array(60)[2]]:=A[list2array(16)[1],list2array(16)[2]];
AA[list2array(61)[1],list2array(61)[2]]:=A[list2array(17)[1],list2array(17)[2]];
AA[list2array(111)[1],list2array(111)[2]]:=A[list2array(69)[1],list2array(69)[2]];
AA[list2array(112)[1],list2array(112)[2]]:=A[list2array(70)[1],list2array(70)[2]];
AA[list2array(113)[1],list2array(113)[2]]:=A[list2array(71)[1],list2array(71)[2]];
AA[list2array(114)[1],list2array(114)[2]]:=A[list2array(72)[1],list2array(72)[2]];
AA[list2array(115)[1],list2array(115)[2]]:=A[list2array(73)[1],list2array(73)[2]];
AA[list2array(116)[1],list2array(116)[2]]:=A[list2array(74)[1],list2array(74)[2]];
AA[list2array(117)[1],list2array(117)[2]]:=A[list2array(75)[1],list2array(75)[2]];
AA[list2array(118)[1],list2array(118)[2]]:=A[list2array(76)[1],list2array(76)[2]];
AA[list2array(119)[1],list2array(119)[2]]:=A[list2array(67)[1],list2array(67)[2]];
AA[list2array(120)[1],list2array(120)[2]]:=A[list2array(68)[1],list2array(68)[2]];
AA[list2array(121)[1],list2array(121)[2]]:=A[list2array(77)[1],list2array(77)[2]];
AA[list2array(122)[1],list2array(122)[2]]:=A[list2array(130)[1],list2array(130)[2]];
AA[list2array(123)[1],list2array(123)[2]]:=A[list2array(131)[1],list2array(131)[2]];
for j from 1 to 26 do
 for i from 1 to nops(templist.j)-2 do
 j1:=list2array(templist.j[i])[1];
 k1:=list2array(templist.j[i])[2];
 j2:=list2array(templist.j[i+1])[1];
 k2:=list2array(templist.j[i+1])[2];
 AA[j1,k1]:=A[j2,k2];
od;
od;
A1:=array(1..12,1..11,[seq([seq(AA[j,i],i=1..11)],j=1..12)]);
RETURN(A1);
end:

move_F2:=proc(A::array)
##
## A is the 11x12 array of colors
## optional argument: [theta,phi] = orientation
##
## rotates SOLID megaminx about f2 facet by 2Pi/5 radians 
## counterclockwise with color array A
## RETURNs new color array AA
##
local AA,A1,i,j,j1,j2,k1,k2,templist;
templist.1:=[12,14,16,18,20,12];
templist.2:=[13,15,17,19,21,13];
templist.3:=[1,60,73,84,31,1];
templist.4:=[2,61,74,85,32,2];
templist.5:=[3,62,75,86,23,3];
templist.6:=[11,66,77,88,33,11];
templist.7:=[4,63,76,87,24,4];
templist.8:=[5,64,67,78,25,5];
templist.9:=[6,65,68,79,26,6];
templist.10:=[7,56,69,80,27,7];
templist.11:=[8,57,70,81,28,8];
templist.12:=[9,58,71,82,29,9];
templist.13:=[10,59,72,83,30,10];
templist.14:=[44,55,121,132,99,44];
templist.15:=[43,52,116,127,98,43];
templist.16:=[42,51,115,126,97,42];
templist.17:=[41,50,114,125,96,41];
templist.18:=[40,49,113,124,95,40];
templist.19:=[39,48,112,123,94,39];
templist.20:=[38,47,111,122,93,38];
templist.21:=[37,46,120,131,92,37];
templist.22:=[36,45,119,130,91,36];
templist.23:=[35,54,118,129,90,35];
templist.24:=[34,53,117,128,89,34];
templist.25:=[108,106,104,102,100,108];
templist.26:=[109,107,105,103,101,109];
for i from 1 to 12 do
 for j from 1 to 11 do
 AA[i,j]:=A[i,j];
 od;
od;
AA[list2array(20)[1],list2array(20)[2]]:=A[list2array(12)[1],list2array(12)[2]];
AA[list2array(21)[1],list2array(21)[2]]:=A[list2array(13)[1],list2array(13)[2]];
AA[list2array(31)[1],list2array(31)[2]]:=A[list2array(1)[1],list2array(1)[2]];
AA[list2array(32)[1],list2array(32)[2]]:=A[list2array(2)[1],list2array(2)[2]];
AA[list2array(23)[1],list2array(23)[2]]:=A[list2array(3)[1],list2array(3)[2]];
AA[list2array(33)[1],list2array(33)[2]]:=A[list2array(11)[1],list2array(11)[2]];
AA[list2array(24)[1],list2array(24)[2]]:=A[list2array(4)[1],list2array(4)[2]];
AA[list2array(25)[1],list2array(25)[2]]:=A[list2array(5)[1],list2array(5)[2]];
AA[list2array(26)[1],list2array(26)[2]]:=A[list2array(6)[1],list2array(6)[2]];
AA[list2array(27)[1],list2array(27)[2]]:=A[list2array(7)[1],list2array(7)[2]];
AA[list2array(28)[1],list2array(28)[2]]:=A[list2array(8)[1],list2array(8)[2]];
AA[list2array(29)[1],list2array(29)[2]]:=A[list2array(9)[1],list2array(9)[2]];
AA[list2array(30)[1],list2array(30)[2]]:=A[list2array(10)[1],list2array(10)[2]];
AA[list2array(99)[1],list2array(99)[2]]:=A[list2array(44)[1],list2array(44)[2]];
AA[list2array(98)[1],list2array(98)[2]]:=A[list2array(43)[1],list2array(43)[2]];
AA[list2array(97)[1],list2array(97)[2]]:=A[list2array(42)[1],list2array(42)[2]];
AA[list2array(96)[1],list2array(96)[2]]:=A[list2array(41)[1],list2array(41)[2]];
AA[list2array(95)[1],list2array(95)[2]]:=A[list2array(40)[1],list2array(40)[2]];
AA[list2array(94)[1],list2array(94)[2]]:=A[list2array(39)[1],list2array(39)[2]];
AA[list2array(93)[1],list2array(93)[2]]:=A[list2array(38)[1],list2array(38)[2]];
AA[list2array(92)[1],list2array(92)[2]]:=A[list2array(37)[1],list2array(37)[2]];
AA[list2array(91)[1],list2array(91)[2]]:=A[list2array(36)[1],list2array(36)[2]];
AA[list2array(90)[1],list2array(90)[2]]:=A[list2array(35)[1],list2array(35)[2]];
AA[list2array(89)[1],list2array(89)[2]]:=A[list2array(34)[1],list2array(34)[2]];
AA[list2array(100)[1],list2array(100)[2]]:=A[list2array(108)[1],list2array(108)[2]];
AA[list2array(101)[1],list2array(101)[2]]:=A[list2array(109)[1],list2array(109)[2]];
for j from 1 to 26 do
 for i from 1 to nops(templist.j)-2 do
 j1:=list2array(templist.j[i])[1];
 k1:=list2array(templist.j[i])[2];
 j2:=list2array(templist.j[i+1])[1];
 k2:=list2array(templist.j[i+1])[2];
 AA[j1,k1]:=A[j2,k2];
od;
od;
A1:=array(1..12,1..11,[seq([seq(AA[j,i],i=1..11)],j=1..12)]);
RETURN(A1);
end:

move_power:=proc(g,A)
local i,j,AA,generators,gen,power;
generators:={f1,f2,f3,f4,f5,f6,F1,F2};
AA:=A;
if type(g,`^`) then 
  gen:=op(1,g);
  power:=op(2,g) mod 5;
 else if member(g,generators) then 
   gen:=g;
   power:=1;
 fi;
fi;
if member(gen,{f1,f2,f3,f4,f5,f6}) then power:=-power mod 5; fi;
if g=1 then RETURN(AA); fi;
for i from 1 to power do
 if gen=f1 then AA:=move_f1(AA) fi;
 if gen=f2 then AA:=move_f2(AA) fi;
 if gen=f3 then AA:=move_f3(AA) fi;
 if gen=f4 then AA:=move_f4(AA) fi;
 if gen=f5 then AA:=move_f5(AA) fi;
 if gen=f6 then AA:=move_f6(AA) fi;
 if gen=F1 then AA:=move_F1(AA) fi;
 if gen=F2 then AA:=move_F2(AA) fi;
od;
RETURN(AA);
end:

move:=proc(w,A)
local i,AA,generators;
generators:={f1,f2,f3,f4,f5,f6,F1,F2};
AA:=A;
if type(w,`^`) then 
  AA:=move_power(w,AA);
fi;
if w=1 then RETURN(AA); fi;
if member(w,generators) then
  AA:=move_power(w,AA);
fi;
if type(w,list) then 
 for i from 1 to nops(w) do
   AA:=move_power(op(i,w),AA);
 od;
fi;
RETURN(AA);
end:

rm := proc (L, A::array) 
##
## L is the move (a list of powers of the generators)
##  A is the 12x11 array of colors
## optional argument: [theta,phi] = orientation
##
local theta,phi;
if nargs=3 then theta:=args[3][1]; phi:=args[3][2]; 
  else theta:=45; phi:=85; 
fi;
faces(evalm(move(L,A)),[theta,phi]); 
end: