##
##
##                    skewb.mpl
##               simulates the moves of the Rubikized octahedron
##
##                                         David Joyner, 1996
###########################################################

A0:=array([[1,1,1,1,1],[2,2,2,2,2],[3,3,3,3,3],
 [4,4,4,4,4],[5,5,5,5,5],[6,6,6,6,6]]);

#basic moves    
FRU:= [[6, 16, 21],[7, 18, 25],[10, 17, 24],[8, 19, 22]]:
BRU:= [[21, 16, 26],[22, 17, 30],[25, 20, 29],[23, 18, 27]]:
BLU:= [[26 ,16, 1],[27, 20, 5],[28, 17, 2],[30, 19, 4]]:
FLU:= [[1, 16, 6],[2, 19, 10],[5, 18, 9],[3, 20, 7]]:
DFR:= [[11, 6, 21],[25, 13, 9],[23, 15, 7],[24, 12, 8]]:
BDR:= [[26, 11, 21],[29, 13, 23],[27, 12, 22],[30, 14, 24]]:
DFL:= [[6, 11, 1],[9, 15, 3],[10, 12, 4],[8, 14, 2]]:
BDL:= [[1, 11, 26],[3, 13, 27],[4, 14, 28],[5, 15, 29]]:
slr:= [[6, 16, 26, 11],[7, 17, 29, 12],[10, 20, 28, 15],
[9,19,27,14],[8,18,30,13],[22,23,24,25],[2,5,4,3]]:
sbf:=[[21,16,1,11],[22,20,4,13],[23,17,5,14],[24,18,2,15],
[25,19,3,12],[7,10,9,8],[30,27,28,29]]:

color1 := red:
color2 := blue:
color3 := coral:
color4 := plum:
color5 := green:
color6 := yellow:

skewb_squares := proc () 
local i; 
for i from 1 to 3 do 
F1.i:=[3,-3+3*(i-1),3]; #i=1,2,3
F3.i:=[3,-3+3*(i-1),-3]; #i=1,2,3
R1.i:=[-3+3*(i-1),3,3];  #i=1,2,3
R3.i:=[-3+3*(i-1),3,-3];  #i=1,2,3
B1.i:=[-3,-3+3*(i-1),3];
B3.i:=[-3,-3+3*(i-1),-3];
L1.i:=[-3+3*(i-1),-3,3];
L3.i:=[-3+3*(i-1),-3,-3];
U1.i:=[-3+3*(i-1),3,3];
U3.i:=[-3+3*(i-1),-3,3];
D1.i:=[-3+3*(i-1),3,-3];
D3.i:=[-3+3*(i-1),-3,-3];
od;
for i from 1 to 2 do 
F2.i:=[3,-3+6*(i-1),0]; #i=1,2
R2.i:=[-3+6*(i-1),3,0];  #i=1,2
B2.i:=[-3,-3+6*(i-1),0];
L2.i:=[-3+6*(i-1),-3,0];
U2.i:=[-3+6*(i-1),0,3];
D2.i:=[-3+6*(i-1),0,-3];
od;
end:

skewb_draw := proc (A::array) 
local i, j, 
face_F0,face_F1,face_F2,face_F3,face_F4,
face_B0,face_B1,face_B2,face_B3,face_B4,
face_L0,face_L1,face_L2,face_L3,face_L4,
face_R0,face_R1,face_R2,face_R3,face_R4,
face_U0,face_U1,face_U2,face_U3,face_U4,
face_D0,face_D1,face_D2,face_D3,face_D4, L; 
skewb_squares();
face_F0:=polygonplot3d([F12,F22,F32,F21],style=patch,
color=color.(A[1,1])); #square
face_F1:=polygonplot3d([F22,F33,F32],style=patch,
color=color.(A[1,2]));
face_F2:=polygonplot3d([F12,F13,F22],style=patch,
color=color.(A[1,3])); 
face_F3:=polygonplot3d([F11,F12,F21],style=patch,
color=color.(A[1,4]));
face_F4:=polygonplot3d([F21,F32,F31],style=patch,
color=color.(A[1,5]));
face_B0:=polygonplot3d([B12,B22,B32,B21],style=patch,
color=color.(A[2,1])); #square
face_B1:=polygonplot3d([B22,B33,B32],style=patch,
color=color.(A[2,2]));
face_B2:=polygonplot3d([B12,B13,B22],style=patch,
color=color.(A[2,3])); 
face_B3:=polygonplot3d([B11,B12,B21],style=patch,
color=color.(A[2,4]));
face_B4:=polygonplot3d([B21,B32,B31],style=patch,
color=color.(A[2,5]));
face_U0:=polygonplot3d([U12,U22,U32,U21],style=patch,
color=color.(A[3,1])); #square
face_U1:=polygonplot3d([U22,U33,U32],style=patch,
color=color.(A[3,2]));
face_U2:=polygonplot3d([U12,U13,U22],style=patch,
color=color.(A[3,3])); 
face_U3:=polygonplot3d([U11,U12,U21],style=patch,
color=color.(A[3,4]));
face_U4:=polygonplot3d([U21,U32,U31],style=patch,
color=color.(A[3,5]));
face_D0:=polygonplot3d([D12,D22,D32,D21],style=patch,
color=color.(A[4,1])); #square
face_D1:=polygonplot3d([D22,D33,D32],style=patch,
color=color.(A[4,2]));
face_D2:=polygonplot3d([D12,D13,D22],style=patch,
color=color.(A[4,3])); 
face_D3:=polygonplot3d([D11,D12,D21],style=patch,
color=color.(A[4,4]));
face_D4:=polygonplot3d([D21,D32,D31],style=patch,
color=color.(A[4,5]));
face_R0:=polygonplot3d([R12,R22,R32,R21],style=patch,
color=color.(A[5,1])); #square
face_R1:=polygonplot3d([R22,R33,R32],style=patch,
color=color.(A[5,2]));
face_R2:=polygonplot3d([R12,R13,R22],style=patch,
color=color.(A[5,3])); 
face_R3:=polygonplot3d([R11,R12,R21],style=patch,
color=color.(A[5,4]));
face_R4:=polygonplot3d([R21,R32,R31],style=patch,
color=color.(A[5,5]));
face_L0:=polygonplot3d([L12,L22,L32,L21],style=patch,
color=color.(A[6,1])); #square
face_L1:=polygonplot3d([L22,L33,L32],style=patch,
color=color.(A[6,2]));
face_L2:=polygonplot3d([L12,L13,L22],style=patch,
color=color.(A[6,3])); 
face_L3:=polygonplot3d([L11,L12,L21],style=patch,
color=color.(A[6,4]));
face_L4:=polygonplot3d([L21,L32,L31],style=patch,
color=color.(A[6,5]));

L:= [face_F0,face_F1,face_F2,face_F3,face_F4,
face_B0,face_B1,face_B2,face_B3,face_B4,
face_L0,face_L1,face_L2,face_L3,face_L4,
face_R0,face_R1,face_R2,face_R3,face_R4,
face_U0,face_U1,face_U2,face_U3,face_U4,
face_D0,face_D1,face_D2,face_D3,face_D4]; 
RETURN(L) 
end:

##skewb move notes

#the move FRU 
fru:=proc(A::array)
local Anew,i,j;
Anew:=array(1..6,1..5);
for i from 1 to 6 do
 for j from 1 to 5 do
   Anew[i,j]:=A[i,j];
 od;
od;
Anew[3,1]:= A[1,1]; #A[1,1] is sent to A[3,1]
Anew[3,2]:= A[1,2];
Anew[3,3]:= A[1,3];
Anew[3,4]:= A[1,4];

Anew[1,1]:= A[5,1];
Anew[1,2]:= A[5,4];
Anew[1,3]:= A[5,3];
Anew[1,4]:= A[5,2];

Anew[5,1]:= A[3,1];
Anew[5,2]:= A[3,4];
Anew[5,3]:= A[3,3];
Anew[5,4]:= A[3,2];

Anew[6,3]:=A[4,3];
Anew[2,3]:=A[6,3];
Anew[4,3]:=A[2,3];
#FUR affects no other pieces
RETURN(Anew);
end:

#the move FLU 
flu:=proc(A::array)
local Anew,i,j;
Anew:=array(1..6,1..5);
for i from 1 to 6 do
 for j from 1 to 5 do
   Anew[i,j]:=A[i,j];
 od;
od;
Anew[6,3]:= A[1,4];
Anew[1,4]:= A[3,2];
Anew[3,2]:= A[6,3];

Anew[1,1]:= A[3,1];
Anew[3,1]:= A[6,1];
Anew[6,1]:= A[1,1];

Anew[1,3]:= A[3,5];
Anew[3,5]:= A[6,2];
Anew[6,2]:= A[1,3];

Anew[1,3]:= A[3,5];
Anew[3,5]:= A[6,2];
Anew[6,2]:= A[1,3];

Anew[1,5]:= A[3,3];
Anew[3,3]:= A[6,4];
Anew[6,4]:= A[1,5];

Anew[4,2]:= A[5,3];
Anew[5,3]:= A[2,4];
Anew[2,4]:= A[4,2];
#LUF affects no other pieces
RETURN(Anew);
end:

#Slr denotes the "spin" of the cube about the R-L axis
slr:=proc(A::array)
local Anew,i,j;
Anew:=array(1..6,1..5);
for i from 1 to 6 do
 for j from 1 to 5 do
   Anew[i,j]:=A[i,j];
 od;
od;
Anew[3,1]:= A[1,1];
Anew[1,1]:= A[4,1];
Anew[4,1]:= A[2,1];
Anew[2,1]:= A[3,1];

Anew[3,4]:= A[1,3];
Anew[1,3]:= A[4,3];
Anew[4,3]:= A[2,2];
Anew[2,2]:= A[3,4];

Anew[3,3]:= A[1,2];
Anew[1,2]:= A[4,4];
Anew[4,4]:= A[2,3];
Anew[2,3]:= A[3,3];

Anew[3,2]:= A[1,5];
Anew[1,5]:= A[4,5];
Anew[4,5]:= A[2,4];
Anew[2,4]:= A[3,2];

Anew[3,5]:= A[1,4];
Anew[1,4]:= A[4,2];
Anew[4,2]:= A[2,5];
Anew[2,5]:= A[3,5];

Anew[5,3]:= A[5,2];
Anew[5,2]:= A[5,5];
Anew[5,5]:= A[5,4];
Anew[5,4]:= A[5,3];

Anew[6,3]:= A[6,2];
Anew[6,2]:= A[6,5];
Anew[6,5]:= A[6,4];
Anew[6,4]:= A[6,3];
#srl affects no other pieces
RETURN(Anew);
end:

dfr:=proc(A::array)
local Anew,i,j;
Anew:=slr(slr(slr(fru(slr(A)))));
RETURN(Anew);
end:

dfl:=proc(A::array)
local Anew,i,j;
Anew:=slr(slr(slr(flu(slr(A)))));
RETURN(Anew);
end:

bru:=proc(A::array)
local Anew,i,j;
Anew:=slr(fru(slr(slr(slr(A)))));
RETURN(Anew);
end:

bdr:=proc(A::array)
local Anew,i,j;
Anew:=slr(slr(fru(slr(slr(A)))));
RETURN(Anew);
end:

blu:=proc(A::array)
local Anew,i,j;
Anew:=slr(flu(slr(slr(slr(A)))));
RETURN(Anew);
end:

bdl:=proc(A::array)
local Anew,i,j;
Anew:=slr(slr(flu(slr(slr(A)))));
RETURN(Anew);
end:

move_power:=proc(g,A::array)
local i,j,AA,generators,gen,power;
generators:={FRU,FLU,BRU,BLU,BDR,BDL,DFR,DFL};
AA:=A;
if type(g,`^`) then 
  gen:=op(1,g);
  power:=op(2,g) mod 3;
 else if member(g,generators) then 
   gen:=g;
   power:=1;
 fi;
fi;
if g=1 then RETURN(A); fi;
for i from 1 to power do
 if gen=FRU then AA:=fru(A) fi;
 if gen=FLU then AA:=flu(A) fi;
 if gen=BRU then AA:=bru(A) fi;
 if gen=BLU then AA:=blu(A) fi;
 if gen=BDR then AA:=bdr(A) fi;
 if gen=BDL then AA:=bdl(A) fi;
 if gen=DFR then AA:=dfr(A) fi;
 if gen=DFL then AA:=dfl(A) fi;
od;
RETURN(AA);
end:

move:=proc(w,A)
local i,AA,generators;
generators:={FRU,FLU,BRU,BLU,BDR,BDL,DFR,DFL};
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:

rs := proc (L, A) local AA, LL; 
AA := move(L,A); LL := skewb_draw(AA); 
display3d(LL) 
end:

help_skewb:=proc()
print(`Moves are generated by FRU,FLU,BRU,BLU,BDR,BDL,DFR,DFL`);
print(`type "rs(1,A0);" to see the solved skewb and, for example,`);
print(`"rs([FRU,FRU,BRU],A0);" to see the move FRU^(-1)*BRU.`);
end: