Pentagon Tiling

Author

Eric W. Weisstein
August 21, 2015

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Tilings/PentagonTiling.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PentagonTiling.html.

©2015 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Demonstration by Ed Pegg Jr.

Figure

http://demonstrations.wolfram.com/PentagonTilings/

Code

enables = 
{{True,True,False,True,True,True,True,True,False,True,True,True,True,False,False},{True,True,False,False,False,False,False,False,False,False,False,False,False,False,False},{True,True,True,True,True,False,False,False,True,False,False,False,False,False,False},{True,False,False,False,False,False,False,False,False,False,False,False,False,False,False},{True,True,False,False,False,False,False,False,False,False,False,False,False,False,False}};

offset[type_,AA_, BB_, b_, c_, e_] := Switch[type,
1,{{-1+b Cos[AA]-e Cos[AA],-b Sin[AA]+e Sin[AA]},{-b Cos[AA]-e Cos[AA]+c Cos[AA+BB],b Sin[AA]+e Sin[AA]-c Sin[AA+BB]}},
2,{{(b/2)-Cos[AA]+(1/2) (b+2 b Cos[AA-BB]-2 Cos[BB]),-Sin[AA]+b Sin[AA-BB]+Sin[BB]},{b+e-2 Cos[AA]+(b-e) Cos[AA-BB],-2 Sin[AA]+(b-e) Sin[AA-BB]}},
3,{{(3/2),((Sqrt[3])/2)},{0,(Sqrt[3])}},
4,{{-1+b (Cos[AA]-Sin[AA]),1-b (Cos[AA]+Sin[AA])},{1-b (Cos[AA]+Sin[AA]),1-b (Cos[AA]-Sin[AA])}},
5,{{(1/2) (3-3 b Cos[AA]+(Sqrt[3]) b Sin[AA]),(1/2) (-(Sqrt[3])+(Sqrt[3]) b Cos[AA]+3 b Sin[AA])},{-(Sqrt[3]) b Sin[AA],(Sqrt[3]) (1-b Cos[AA])}},
6,{{-1-2 Cos[(AA/2)]+Cos[((3 AA)/2)],2 Sin[(AA/2)]-Sin[((3 AA)/2)]},{(1/2)-Cos[(AA/2)]-2 Cos[AA],(1/2) Cot[(AA/4)]+Sin[(AA/2)]+2 Sin[AA]}},
7,{{1+((2 Cos[AA])/(-2-Cos[AA]+Cos[3 AA])),((Sin[AA]-Sin[3 AA])/(2+Cos[AA]-Cos[3 AA]))},{-((Sin[2 AA] Sin[4 AA])/(2+Cos[AA]-Cos[3 AA])),((-4 Sin[AA]+Sin[2 AA]-4 Sin[3 AA]+2 Sin[4 AA]+Sin[6 AA])/(2 (2+Cos[AA]-Cos[3 AA])))}},
8,{{((12 ((Cos[(AA/4)])^2) (Cos[(AA/2)]+2 Cos[AA]))/(5+4 Cos[(AA/2)])),((3 (4 Sin[(AA/2)]+5 Sin[AA]+2 Sin[((3 AA)/2)]))/(5+4 Cos[(AA/2)]))},{((11+22 Cos[(AA/2)]+11 Cos[AA]-4 Cos[((3 AA)/2)]-4 Cos[2 AA])/(5+4 Cos[(AA/2)])),((18 Sin[(AA/2)]+11 Sin[AA]-4 (Sin[((3 AA)/2)]+Sin[2 AA]))/(5+4 Cos[(AA/2)]))}},
9,{{((4 (-1+(b^2)))/(8-5 (b^2)+(b^4))),((4 (-3+(b^2)) (Sqrt[-1+(b^2)]))/(8-5 (b^2)+(b^4)))},{-4+(12/(b^2))+((8 (-5+2 (b^2)))/(8-5 (b^2)+(b^4))),((4 (Sqrt[-1+(b^2)]) (8-11 (b^2)+2 (b^4)))/((b^2) (8-5 (b^2)+(b^4))))}},
10,{{-3+3 Cos[AA]+(6/(1+Cot[(AA/2)]))+Sin[AA],((1+2 Cos[AA]+4 Sin[AA])/(1+Cot[(AA/2)]))},{((3-4 Cos[AA])/(1+Tan[(AA/2)])),-((Sin[(AA/2)]+2 Sin[((3 AA)/2)])/(Cos[(AA/2)]+Sin[(AA/2)]))}},
11,{{((8 Cos[AA] ((Sin[AA])^3))/(-1+2 Cos[AA])),-((8 (-1+Cos[AA]) Cos[AA] ((Sin[AA])^2))/(-1+2 Cos[AA]))},{(((3-8 Cos[AA]+4 Cos[2 AA]) Sin[AA])/(-1+2 Cos[AA])),((1+3 Cos[AA]-2 Cos[3 AA])/(-1+2 Cos[AA]))}},
12,{{Cot[(AA/4)]+((2 (3+4 Cos[(AA/2)]) Sin[AA])/(1+2 Cos[(AA/2)])),-8-10 Cos[(AA/2)]+(1/(1+2 Cos[(AA/2)]))-4 Cos[AA]+2 ((Csc[(AA/4)])^2)},{3 Cot[(AA/4)]-2 Sin[(AA/2)],1+2 Cos[(AA/2)]}},
13,{{1-Cos[AA]-Sin[AA],-1+Cos[AA]-Sin[AA]},{3 (-1+Cos[AA])-3 Sin[AA],3 (-1+Cos[AA])+3 Sin[AA]}},
14,{{(1/2) (1-(Sqrt[57])),Root[-72-15 ((#1)^2)+((#1)^4)&,2]},{(1/16) (21+(Sqrt[57])),Root[-31752-639 ((#1)^2)+64 ((#1)^4)&,2]}},
15, {{1+(Sqrt[3]),3+(Sqrt[3])}/4,{-8-5 (Sqrt[3]),9+4 (Sqrt[3])}/4}];

motif[type_,AA_, BB_, b_, c_, e_] := Switch[type,
1,
{{{(1/2)-b Cos[AA],b Sin[AA]},{(1/2)-b Cos[AA]+c Cos[AA+BB],b Sin[AA]-c Sin[AA+BB]},{-(1/2)-e Cos[AA],e Sin[AA]},{-(1/2),0},{(1/2),0}},{{-(1/2)+b Cos[AA],-b Sin[AA]},{-(1/2)+b Cos[AA]-c Cos[AA+BB],-b Sin[AA]+c Sin[AA+BB]},{(1/2)+e Cos[AA],-e Sin[AA]},{(1/2),0},{-(1/2),0}}},
2,
{{{(1/2) (b-2 Cos[BB]),Sin[BB]},{-(b/2)+Cos[AA]+e Cos[AA-BB],Sin[AA]+e Sin[AA-BB]},{-(b/2)+Cos[AA],Sin[AA]},{-(b/2),0},{(b/2),0}},{{(1/2) (b-2 Cos[AA]+2 b Cos[AA-BB]-2 Cos[BB]),-Sin[AA]+b Sin[AA-BB]+Sin[BB]},{(b/2)+e,0},{(b/2),0},{(1/2) (b-2 Cos[BB]),Sin[BB]},{(1/2) (b+2 b Cos[AA-BB]-2 Cos[BB]),b Sin[AA-BB]+Sin[BB]}},{{-(b/2)+Cos[AA]+e Cos[AA-BB],Sin[AA]+e Sin[AA-BB]},{(1/2) (b-2 Cos[BB]),Sin[BB]},{(b/2)+e Cos[AA-BB]-Cos[BB],e Sin[AA-BB]+Sin[BB]},{(b/2)+Cos[AA]+e Cos[AA-BB]-Cos[BB],Sin[AA]+e Sin[AA-BB]+Sin[BB]},{-(b/2)+Cos[AA]+e Cos[AA-BB]-Cos[BB],Sin[AA]+e Sin[AA-BB]+Sin[BB]}},{{-(b/2)+2 Cos[AA]+(-b+e) Cos[AA-BB],2 Sin[AA]+(-b+e) Sin[AA-BB]},{-(b/2)-e+Cos[AA]+e Cos[AA-BB]-Cos[BB],Sin[AA]+e Sin[AA-BB]+Sin[BB]},{-(b/2)+Cos[AA]+e Cos[AA-BB]-Cos[BB],Sin[AA]+e Sin[AA-BB]+Sin[BB]},{-(b/2)+Cos[AA]+e Cos[AA-BB],Sin[AA]+e Sin[AA-BB]},{-(b/2)+Cos[AA]+(-b+e) Cos[AA-BB],Sin[AA]+(-b+e) Sin[AA-BB]}}},
3,
{{{0,0},{(1/2),((Sqrt[3])/2)},{(b/2),-(1/2) (Sqrt[3]) (-2+b)},{-(1/2),((Sqrt[3])/2)},{-b,0}},{{-(3/2),((Sqrt[3])/2)},{-1,0},{-b,0},{-(1/2),((Sqrt[3])/2)},{(1/2) (-3+b),(1/2) (Sqrt[3]) (1+b)}},{{0,(Sqrt[3])},{-1,(Sqrt[3])},{(1/2) (-3+b),(1/2) (Sqrt[3]) (1+b)},{-(1/2),((Sqrt[3])/2)},{(b/2),-(1/2) (Sqrt[3]) (-2+b)}}},
4,
{{{0,0},{0,1},{-b Sin[AA],1-b Cos[AA]},{b (Cos[AA]-Sin[AA]),1-b (Cos[AA]+Sin[AA])},{-1,0}},{{0,0},{-1,0},{-1+b Cos[AA],-b Sin[AA]},{-1+b (Cos[AA]+Sin[AA]),b (Cos[AA]-Sin[AA])},{0,-1}},{{0,0},{0,-1},{b Sin[AA],-1+b Cos[AA]},{-b (Cos[AA]-Sin[AA]),-1+b (Cos[AA]+Sin[AA])},{1,0}},{{0,0},{1,0},{1-b Cos[AA],b Sin[AA]},{1-b (Cos[AA]+Sin[AA]),-b (Cos[AA]-Sin[AA])},{0,1}}},
5,
{{{0,0},{1,0},{1-b Cos[AA],b Sin[AA]},{(1/2) (2-3 b Cos[AA]-(Sqrt[3]) b Sin[AA]),-(1/2) b ((Sqrt[3]) Cos[AA]-3 Sin[AA])},{(1/2),((Sqrt[3])/2)}},{{0,0},{(1/2),((Sqrt[3])/2)},{(1/2) (1-b (Cos[AA]+(Sqrt[3]) Sin[AA])),(1/2) ((Sqrt[3]) (1-b Cos[AA])+b Sin[AA])},{(1/2)-(Sqrt[3]) b Sin[AA],(1/2) (Sqrt[3]) (1-2 b Cos[AA])},{-(1/2),((Sqrt[3])/2)}},{{0,0},{-(1/2),((Sqrt[3])/2)},{(1/2) (-1+b Cos[AA]-(Sqrt[3]) b Sin[AA]),(1/2) ((Sqrt[3]) (1-b Cos[AA])-b Sin[AA])},{(1/2) (-1+3 b Cos[AA]-(Sqrt[3]) b Sin[AA]),(1/2) ((Sqrt[3])-(Sqrt[3]) b Cos[AA]-3 b Sin[AA])},{-1,0}},{{0,0},{-1,0},{-1+b Cos[AA],-b Sin[AA]},{(1/2) (-2+3 b Cos[AA]+(Sqrt[3]) b Sin[AA]),(1/2) b ((Sqrt[3]) Cos[AA]-3 Sin[AA])},{-(1/2),-((Sqrt[3])/2)}},{{0,0},{-(1/2),-((Sqrt[3])/2)},{(1/2) (-1+b Cos[AA]+(Sqrt[3]) b Sin[AA]),(1/2) ((Sqrt[3]) (-1+b Cos[AA])-b Sin[AA])},{-(1/2)+(Sqrt[3]) b Sin[AA],(1/2) (Sqrt[3]) (-1+2 b Cos[AA])},{(1/2),-((Sqrt[3])/2)}},{{0,0},{(1/2),-((Sqrt[3])/2)},{(1/2) (1-b Cos[AA]+(Sqrt[3]) b Sin[AA]),(1/2) ((Sqrt[3]) (-1+b Cos[AA])+b Sin[AA])},{(1/2) (1-3 b Cos[AA]+(Sqrt[3]) b Sin[AA]),(1/2) (-(Sqrt[3])+(Sqrt[3]) b Cos[AA]+3 b Sin[AA])},{1,0}}},
6,
{{{(1/2),0},{(1/2)-Cos[AA],Sin[AA]},{-Cos[(AA/2)]-Cos[AA],(1/2) Cot[(AA/4)]+Sin[(AA/2)]+Sin[AA]},{-(1/2)-Cos[(AA/2)],Sin[(AA/2)]},{-(1/2),0}},{{-(1/2)-Cos[(AA/2)],Sin[(AA/2)]},{-(1/2)-Cos[(AA/2)]+Cos[((3 AA)/2)],Sin[(AA/2)]-Sin[((3 AA)/2)]},{-1-Cos[(AA/2)]+Cos[AA]+Cos[((3 AA)/2)],(1/2) (-2 Cos[((3 AA)/4)]+Cos[((7 AA)/4)]) Csc[(AA/4)]},{-(1/2)+Cos[AA],-Sin[AA]},{-(1/2),0}},{{-(1/2),0},{-(1/2)+Cos[AA],-Sin[AA]},{Cos[(AA/2)]+Cos[AA],-(1/2) Cot[(AA/4)]-Sin[(AA/2)]-Sin[AA]},{(1/2)+Cos[(AA/2)],-Sin[(AA/2)]},{(1/2),0}},{{(1/2)+Cos[(AA/2)],-Sin[(AA/2)]},{(1/2)+Cos[(AA/2)]-Cos[((3 AA)/2)],-Sin[(AA/2)]+Sin[((3 AA)/2)]},{1+Cos[(AA/2)]-Cos[AA]-Cos[((3 AA)/2)],-(1/2) (-2 Cos[((3 AA)/4)]+Cos[((7 AA)/4)]) Csc[(AA/4)]},{(1/2)-Cos[AA],Sin[AA]},{(1/2),0}}},
7,
{{{1-((Cos[AA])/2),((Sin[AA])/2)},{-((Cos[AA])/2),((Sin[AA])/2)},{((Cos[AA])/2),-((Sin[AA])/2)},{-((Cos[AA])/2),-((3 Sin[AA])/2)},{-((-1+4 Cos[AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((-2 Sin[2 AA]-4 Sin[3 AA]+Sin[4 AA])/(4 (2+Cos[AA]-Cos[3 AA])))}},{{-((-1+4 Cos[AA]-8 Cos[2 AA]-2 Cos[3 AA]+Cos[4 AA]+2 Cos[5 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((4 Sin[AA]+6 Sin[2 AA]-2 Sin[3 AA]+Sin[4 AA]-2 Sin[5 AA])/(8+4 Cos[AA]-4 Cos[3 AA]))},{-((-3+2 Cos[3 AA]+3 Cos[4 AA]+2 Cos[5 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),-((-2 Sin[2 AA]+6 Sin[3 AA]+Sin[4 AA]+2 Sin[5 AA])/(4 (2+Cos[AA]-Cos[3 AA])))},{((-1+4 Cos[3 AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((-4 Sin[AA]+2 Sin[2 AA]+3 Sin[4 AA])/(4 (2+Cos[AA]-Cos[3 AA])))},{-((Cos[AA])/2),-((3 Sin[AA])/2)},{-((-1+4 Cos[AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((-2 Sin[2 AA]-4 Sin[3 AA]+Sin[4 AA])/(4 (2+Cos[AA]-Cos[3 AA])))}},{{-((Cos[AA])/2),-((3 Sin[AA])/2)},{((Cos[AA])/2),-((Sin[AA])/2)},{(1/2) (-2+Cos[AA]),-((Sin[AA])/2)},{-1+((Cos[AA])/2)+Cos[2 AA],-((Sin[AA])/2)+Sin[2 AA]},{((-1+4 Cos[3 AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((-4 Sin[AA]+2 Sin[2 AA]+3 Sin[4 AA])/(4 (2+Cos[AA]-Cos[3 AA])))}},{{-((-1+2 Cos[2 AA]+4 Cos[3 AA]+Cos[4 AA]-2 Cos[6 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((-4 Sin[AA]-8 Sin[3 AA]+Sin[4 AA]+2 Sin[6 AA])/(4 (2+Cos[AA]-Cos[3 AA])))},{((Cos[AA] (-3 Cos[AA]+Cos[3 AA]+2 (Cos[4 AA]+Cos[5 AA])))/(2 (2+Cos[AA]-Cos[3 AA]))),((-8 Sin[AA]-2 Sin[3 AA]+5 Sin[4 AA]+2 (Sin[5 AA]+Sin[6 AA]))/(4 (2+Cos[AA]-Cos[3 AA])))},{((5-4 Cos[AA]-2 Cos[3 AA]+3 Cos[4 AA]+2 Cos[5 AA])/(4 (-2-Cos[AA]+Cos[3 AA]))),-((4 Sin[AA]-2 Sin[2 AA]+2 Sin[3 AA]+Sin[4 AA]+2 Sin[5 AA])/(4 (2+Cos[AA]-Cos[3 AA])))},{-1+((Cos[AA])/2)+Cos[2 AA],-((Sin[AA])/2)+Sin[2 AA]},{((-1+4 Cos[3 AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((-4 Sin[AA]+2 Sin[2 AA]+3 Sin[4 AA])/(4 (2+Cos[AA]-Cos[3 AA])))}},{{(1/2) (-2+Cos[AA]),-((Sin[AA])/2)},{((Cos[AA])/2),-((Sin[AA])/2)},{-((Cos[AA])/2),((Sin[AA])/2)},{((Cos[AA])/2),((3 Sin[AA])/2)},{((-1+4 Cos[AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((2 Sin[2 AA]+4 Sin[3 AA]-Sin[4 AA])/(8+4 Cos[AA]-4 Cos[3 AA]))}},{{((-1+4 Cos[AA]-8 Cos[2 AA]-2 Cos[3 AA]+Cos[4 AA]+2 Cos[5 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),-((4 Sin[AA]+6 Sin[2 AA]-2 Sin[3 AA]+Sin[4 AA]-2 Sin[5 AA])/(4 (2+Cos[AA]-Cos[3 AA])))},{((Cos[AA] (-3 Cos[AA]+3 Cos[3 AA]+2 Cos[4 AA]))/(2 (2+Cos[AA]-Cos[3 AA]))),((-2 Sin[2 AA]+6 Sin[3 AA]+Sin[4 AA]+2 Sin[5 AA])/(4 (2+Cos[AA]-Cos[3 AA])))},{-((-1+4 Cos[3 AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((4 Sin[AA]-2 Sin[2 AA]-3 Sin[4 AA])/(8+4 Cos[AA]-4 Cos[3 AA]))},{((Cos[AA])/2),((3 Sin[AA])/2)},{((-1+4 Cos[AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((2 Sin[2 AA]+4 Sin[3 AA]-Sin[4 AA])/(8+4 Cos[AA]-4 Cos[3 AA]))}},{{((Cos[AA])/2),((3 Sin[AA])/2)},{-((Cos[AA])/2),((Sin[AA])/2)},{1-((Cos[AA])/2),((Sin[AA])/2)},{-((Cos[AA])/2)+2 ((Sin[AA])^2),(1/2) (1-4 Cos[AA]) Sin[AA]},{-((-1+4 Cos[3 AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((4 Sin[AA]-2 Sin[2 AA]-3 Sin[4 AA])/(8+4 Cos[AA]-4 Cos[3 AA]))}},{{((-1+2 Cos[2 AA]+4 Cos[3 AA]+Cos[4 AA]-2 Cos[6 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),-((-4 Sin[AA]-8 Sin[3 AA]+Sin[4 AA]+2 Sin[6 AA])/(4 (2+Cos[AA]-Cos[3 AA])))},{-((Cos[AA] (-3 Cos[AA]+Cos[3 AA]+2 (Cos[4 AA]+Cos[5 AA])))/(2 (2+Cos[AA]-Cos[3 AA]))),((8 Sin[AA]+2 Sin[3 AA]-5 Sin[4 AA]-2 (Sin[5 AA]+Sin[6 AA]))/(4 (2+Cos[AA]-Cos[3 AA])))},{((5-4 Cos[AA]-2 Cos[3 AA]+3 Cos[4 AA]+2 Cos[5 AA])/(8+4 Cos[AA]-4 Cos[3 AA])),((4 Sin[AA]-2 Sin[2 AA]+2 Sin[3 AA]+Sin[4 AA]+2 Sin[5 AA])/(8+4 Cos[AA]-4 Cos[3 AA]))},{-((Cos[AA])/2)+2 ((Sin[AA])^2),(1/2) (1-4 Cos[AA]) Sin[AA]},{-((-1+4 Cos[3 AA]+Cos[4 AA])/(4 (2+Cos[AA]-Cos[3 AA]))),((4 Sin[AA]-2 Sin[2 AA]-3 Sin[4 AA])/(8+4 Cos[AA]-4 Cos[3 AA]))}}},
8,
{{{-(1/2),0},{(1/2),0},{(1/2)-Cos[AA],-Sin[AA]},{-(3/4)+(9/(4 (5+4 Cos[(AA/2)])))-Cos[AA],((-5 (Sin[(AA/2)]+Sin[AA])-2 Sin[((3 AA)/2)])/(5+4 Cos[(AA/2)]))},{-(1/2)-Cos[(AA/2)],-Sin[(AA/2)]}},{{-((11+22 Cos[(AA/2)]+12 Cos[AA])/(10+8 Cos[(AA/2)])),-((3 (3 Sin[(AA/2)]+2 Sin[AA]))/(5+4 Cos[(AA/2)]))},{-((11+24 Cos[(AA/2)]+20 Cos[AA]+8 Cos[((3 AA)/2)])/(10+8 Cos[(AA/2)])),-((2 (5 (Sin[(AA/2)]+Sin[AA])+2 Sin[((3 AA)/2)]))/(5+4 Cos[(AA/2)]))},{-((3+14 Cos[(AA/2)]+20 Cos[AA]+8 Cos[((3 AA)/2)])/(10+8 Cos[(AA/2)])),-(((11+20 Cos[(AA/2)]+8 Cos[AA]) Sin[(AA/2)])/(5+4 Cos[(AA/2)]))},{-((3+10 Cos[(AA/2)]+10 Cos[AA]+4 Cos[((3 AA)/2)])/(10+8 Cos[(AA/2)])),((-5 (Sin[(AA/2)]+Sin[AA])-2 Sin[((3 AA)/2)])/(5+4 Cos[(AA/2)]))},{-(1/2)-Cos[(AA/2)],-Sin[(AA/2)]}},{{(1/2),0},{-(1/2),0},{-(1/2)+Cos[AA],Sin[AA]},{(3/4)-(9/(4 (5+4 Cos[(AA/2)])))+Cos[AA],((5 (Sin[(AA/2)]+Sin[AA])+2 Sin[((3 AA)/2)])/(5+4 Cos[(AA/2)]))},{(1/2)+Cos[(AA/2)],Sin[(AA/2)]}},{{((11+22 Cos[(AA/2)]+12 Cos[AA])/(10+8 Cos[(AA/2)])),((9 Sin[(AA/2)]+6 Sin[AA])/(5+4 Cos[(AA/2)]))},{((11+24 Cos[(AA/2)]+20 Cos[AA]+8 Cos[((3 AA)/2)])/(10+8 Cos[(AA/2)])),((2 (5 (Sin[(AA/2)]+Sin[AA])+2 Sin[((3 AA)/2)]))/(5+4 Cos[(AA/2)]))},{((3+14 Cos[(AA/2)]+20 Cos[AA]+8 Cos[((3 AA)/2)])/(10+8 Cos[(AA/2)])),(((11+20 Cos[(AA/2)]+8 Cos[AA]) Sin[(AA/2)])/(5+4 Cos[(AA/2)]))},{((3+10 Cos[(AA/2)]+10 Cos[AA]+4 Cos[((3 AA)/2)])/(10+8 Cos[(AA/2)])),((5 (Sin[(AA/2)]+Sin[AA])+2 Sin[((3 AA)/2)])/(5+4 Cos[(AA/2)]))},{(1/2)+Cos[(AA/2)],Sin[(AA/2)]}},{{-(1/2),0},{-(1/2)-Cos[(AA/2)],-Sin[(AA/2)]},{-(1/2)-Cos[(AA/2)]+Cos[((3 AA)/2)],2 Cos[AA] Sin[(AA/2)]},{((-7-6 Cos[(AA/2)]+8 Cos[AA]+10 Cos[((3 AA)/2)]+4 Cos[2 AA])/(10+8 Cos[(AA/2)])),((-Sin[(AA/2)]+4 Sin[AA]+5 Sin[((3 AA)/2)]+2 Sin[2 AA])/(5+4 Cos[(AA/2)]))},{-(1/2)+Cos[AA],Sin[AA]}},{{((-11-22 Cos[(AA/2)]-10 Cos[AA]+8 Cos[((3 AA)/2)]+8 Cos[2 AA])/(10+8 Cos[(AA/2)])),(((-5+8 Cos[AA]) (Sin[(AA/2)]+Sin[AA]))/(5+4 Cos[(AA/2)]))},{-((11+22 Cos[(AA/2)]+12 Cos[AA])/(10+8 Cos[(AA/2)])),-((3 (3 Sin[(AA/2)]+2 Sin[AA]))/(5+4 Cos[(AA/2)]))},{-(1/2)-Cos[(AA/2)],-Sin[(AA/2)]},{-(1/2)-Cos[(AA/2)]+Cos[((3 AA)/2)],2 Cos[AA] Sin[(AA/2)]},{((-11-20 Cos[(AA/2)]-2 Cos[AA]+16 Cos[((3 AA)/2)]+8 Cos[2 AA])/(10+8 Cos[(AA/2)])),((2 (3 Cos[(AA/2)]+8 Cos[AA]+4 Cos[((3 AA)/2)]) Sin[(AA/2)])/(5+4 Cos[(AA/2)]))}},{{(1/2),0},{(1/2)+Cos[(AA/2)],Sin[(AA/2)]},{(1/2)+Cos[(AA/2)]-Cos[((3 AA)/2)],-2 Cos[AA] Sin[(AA/2)]},{((7+6 Cos[(AA/2)]-8 Cos[AA]-10 Cos[((3 AA)/2)]-4 Cos[2 AA])/(10+8 Cos[(AA/2)])),((Sin[(AA/2)]-4 Sin[AA]-5 Sin[((3 AA)/2)]-2 Sin[2 AA])/(5+4 Cos[(AA/2)]))},{(1/2)-Cos[AA],-Sin[AA]}},{{((11+22 Cos[(AA/2)]+10 Cos[AA]-8 Cos[((3 AA)/2)]-8 Cos[2 AA])/(10+8 Cos[(AA/2)])),-(((-5+8 Cos[AA]) (Sin[(AA/2)]+Sin[AA]))/(5+4 Cos[(AA/2)]))},{((11+22 Cos[(AA/2)]+12 Cos[AA])/(10+8 Cos[(AA/2)])),((9 Sin[(AA/2)]+6 Sin[AA])/(5+4 Cos[(AA/2)]))},{(1/2)+Cos[(AA/2)],Sin[(AA/2)]},{(1/2)+Cos[(AA/2)]-Cos[((3 AA)/2)],-2 Cos[AA] Sin[(AA/2)]},{((11+20 Cos[(AA/2)]+2 Cos[AA]-16 Cos[((3 AA)/2)]-8 Cos[2 AA])/(10+8 Cos[(AA/2)])),((8 Sin[(AA/2)]+Sin[AA]-4 (2 Sin[((3 AA)/2)]+Sin[2 AA]))/(5+4 Cos[(AA/2)]))}}},
9,
{{{0,-(Sqrt[-1+(b^2)])},{-1+(2/(b^2))+((2 (-1+(b^2)))/(8-5 (b^2)+(b^4))),((4 (-4+(b^2)) (Sqrt[-1+(b^2)]))/((b^2) (8-5 (b^2)+(b^4))))},{2 (-1+(1/(b^2))+((-1+(b^2))/(8-5 (b^2)+(b^4)))),-(((Sqrt[-1+(b^2)]) (16+4 (b^2)-5 (b^4)+(b^6)))/((b^2) (8-5 (b^2)+(b^4))))},{-2+(4/(b^2)),(-1-(4/(b^2))) (Sqrt[-1+(b^2)])},{-3+(4/(b^2)),-((4 (Sqrt[-1+(b^2)]))/(b^2))}},{{4 (-1+(1/(b^2))+((-1+(b^2))/(8-5 (b^2)+(b^4)))),-(((Sqrt[-1+(b^2)]) (32-5 (b^4)+(b^6)))/((b^2) (8-5 (b^2)+(b^4))))},{-3+(4/(b^2))+((4 (-1+(b^2)))/(8-5 (b^2)+(b^4))),((8 (-4+(b^2)) (Sqrt[-1+(b^2)]))/((b^2) (8-5 (b^2)+(b^4))))},{2 (-1+(1/(b^2))+((-1+(b^2))/(8-5 (b^2)+(b^4)))),-(((Sqrt[-1+(b^2)]) (16+4 (b^2)-5 (b^4)+(b^6)))/((b^2) (8-5 (b^2)+(b^4))))},{-2+(4/(b^2)),(-1-(4/(b^2))) (Sqrt[-1+(b^2)])},{-1+(4/(b^2))+((4 (-3+(b^2)))/(8-5 (b^2)+(b^4))),-((4 (Sqrt[-1+(b^2)]) (8-4 (b^2)+(b^4)))/((b^2) (8-5 (b^2)+(b^4))))}},{{1,0},{0,-(Sqrt[-1+(b^2)])},{-1+(2/(b^2))+((2 (-1+(b^2)))/(8-5 (b^2)+(b^4))),((4 (-4+(b^2)) (Sqrt[-1+(b^2)]))/((b^2) (8-5 (b^2)+(b^4))))},{-1+((4 (-1+(b^2)))/(8-5 (b^2)+(b^4))),((4 (-3+(b^2)) (Sqrt[-1+(b^2)]))/(8-5 (b^2)+(b^4)))},{-2+(8/(8-5 (b^2)+(b^4))),-(((Sqrt[-1+(b^2)]) (16-9 (b^2)+(b^4)))/(8-5 (b^2)+(b^4)))}},{{-3+(4/(b^2))+((4 (-1+(b^2)))/(8-5 (b^2)+(b^4))),((8 (-4+(b^2)) (Sqrt[-1+(b^2)]))/((b^2) (8-5 (b^2)+(b^4))))},{2 (-1+(1/(b^2))+((-1+(b^2))/(8-5 (b^2)+(b^4)))),-(((Sqrt[-1+(b^2)]) (16+4 (b^2)-5 (b^4)+(b^6)))/((b^2) (8-5 (b^2)+(b^4))))},{-1+(2/(b^2))+((2 (-1+(b^2)))/(8-5 (b^2)+(b^4))),((4 (-4+(b^2)) (Sqrt[-1+(b^2)]))/((b^2) (8-5 (b^2)+(b^4))))},{-1+((4 (-1+(b^2)))/(8-5 (b^2)+(b^4))),((4 (-3+(b^2)) (Sqrt[-1+(b^2)]))/(8-5 (b^2)+(b^4)))},{((4 (-1+(b^2)))/(8-5 (b^2)+(b^4))),-(((Sqrt[-1+(b^2)]) (20-9 (b^2)+(b^4)))/(8-5 (b^2)+(b^4)))}},{{-6+(12/(b^2))+((4 (-7+3 (b^2)))/(8-5 (b^2)+(b^4))),-(((Sqrt[-1+(b^2)]) (-32+48 (b^2)-13 (b^4)+(b^6)))/((b^2) (8-5 (b^2)+(b^4))))},{-3+(8/(b^2))+((4 (-7+3 (b^2)))/(8-5 (b^2)+(b^4))),((4 (-5+(b^2)) (Sqrt[-1+(b^2)]))/(8-5 (b^2)+(b^4)))},{-4+(8/(b^2))+((8 (-2+(b^2)))/(8-5 (b^2)+(b^4))),-(((Sqrt[-1+(b^2)]) (24-9 (b^2)+(b^4)))/(8-5 (b^2)+(b^4)))},{4 (-1+(1/(b^2))+((-1+(b^2))/(8-5 (b^2)+(b^4)))),-(((Sqrt[-1+(b^2)]) (32-5 (b^4)+(b^6)))/((b^2) (8-5 (b^2)+(b^4))))},{-1+(4/(b^2))+((4 (-3+(b^2)))/(8-5 (b^2)+(b^4))),-((4 (Sqrt[-1+(b^2)]) (8-4 (b^2)+(b^4)))/((b^2) (8-5 (b^2)+(b^4))))}},{{-2+(4/(b^2))+((4 (-1+(b^2)))/(8-5 (b^2)+(b^4))),-(((Sqrt[-1+(b^2)]) (32-5 (b^4)+(b^6)))/((b^2) (8-5 (b^2)+(b^4))))},{-1+(4/(b^2))+((8 (-2+(b^2)))/(8-5 (b^2)+(b^4))),((4 (-8+(b^2)) (Sqrt[-1+(b^2)]))/((b^2) (8-5 (b^2)+(b^4))))},{-4+(8/(b^2))+((8 (-2+(b^2)))/(8-5 (b^2)+(b^4))),-(((Sqrt[-1+(b^2)]) (24-9 (b^2)+(b^4)))/(8-5 (b^2)+(b^4)))},{4 (-1+(1/(b^2))+((-1+(b^2))/(8-5 (b^2)+(b^4)))),-(((Sqrt[-1+(b^2)]) (32-5 (b^4)+(b^6)))/((b^2) (8-5 (b^2)+(b^4))))},{-3+(4/(b^2))+((4 (-1+(b^2)))/(8-5 (b^2)+(b^4))),((8 (-4+(b^2)) (Sqrt[-1+(b^2)]))/((b^2) (8-5 (b^2)+(b^4))))}},{{3-(8/(b^2))-((8 (-3+(b^2)))/(8-5 (b^2)+(b^4))),-((8 (Sqrt[-1+(b^2)]) (8-6 (b^2)+(b^4)))/((b^2) (8-5 (b^2)+(b^4))))},{-(4/(b^2))-((8 (-3+(b^2)))/(8-5 (b^2)+(b^4))),(((Sqrt[-1+(b^2)]) (-32+20 (b^2)+(b^4)-(b^6)))/((b^2) (8-5 (b^2)+(b^4))))},{1-(4/(b^2))-((4 (-3+(b^2)))/(8-5 (b^2)+(b^4))),-((4 (Sqrt[-1+(b^2)]) (8-6 (b^2)+(b^4)))/((b^2) (8-5 (b^2)+(b^4))))},{1,0},{-2+(8/(8-5 (b^2)+(b^4))),-(((Sqrt[-1+(b^2)]) (16-9 (b^2)+(b^4)))/(8-5 (b^2)+(b^4)))}},{{-1,0},{-2-((4 (-3+(b^2)))/(8-5 (b^2)+(b^4))),-(((Sqrt[-1+(b^2)]) (4-5 (b^2)+(b^4)))/(8-5 (b^2)+(b^4)))},{1-(4/(b^2))-((4 (-3+(b^2)))/(8-5 (b^2)+(b^4))),-((4 (Sqrt[-1+(b^2)]) (8-6 (b^2)+(b^4)))/((b^2) (8-5 (b^2)+(b^4))))},{1,0},{0,-(Sqrt[-1+(b^2)])}}},
10,
{{{1,0},{(1/2) (-1+Cos[AA]+3 Sin[AA]),-((-2+2 Cos[AA]+Sin[AA])/(1+Tan[(AA/2)]))},{Sin[AA] (-1+(3/(1+Tan[(AA/2)]))),(1/2) (-1-Cos[AA]+3 Sin[AA])},{0,1},{0,0}},{{0,1},{((-2+2 Cos[AA]+Sin[AA])/(1+Tan[(AA/2)])),(1/2) (-1+Cos[AA]+3 Sin[AA])},{(1/2) (1+Cos[AA]-3 Sin[AA]),Sin[AA] (-1+(3/(1+Tan[(AA/2)])))},{-1,0},{0,0}},{{-1,0},{(1/2) (1-Cos[AA]-3 Sin[AA]),((-2+2 Cos[AA]+Sin[AA])/(1+Tan[(AA/2)]))},{Sin[AA] (1-(3/(1+Tan[(AA/2)]))),(1/2) (1+Cos[AA]-3 Sin[AA])},{0,-1},{0,0}},{{0,-1},{-((-2+2 Cos[AA]+Sin[AA])/(1+Tan[(AA/2)])),(1/2) (1-Cos[AA]-3 Sin[AA])},{(1/2) (-1-Cos[AA]+3 Sin[AA]),Sin[AA] (1-(3/(1+Tan[(AA/2)])))},{1,0},{0,0}},{{(1/2) (-3+Cos[AA]+(6/(1+Cot[(AA/2)]))+3 Sin[AA]),-((Cos[(AA/2)] (-2+2 Cos[AA]+Sin[AA]))/(Cos[(AA/2)]+Sin[(AA/2)]))},{(1/2) (-1+Cos[AA]+3 Sin[AA]),-((-2+2 Cos[AA]+Sin[AA])/(1+Tan[(AA/2)]))},{((-1+Cos[AA]+2 Sin[AA])/(1+Tan[(AA/2)])),(1/2) (-1-Cos[AA]+3 Sin[AA])},{((Cos[(AA/2)] (-1+Cos[AA]+2 Sin[AA]))/(Cos[(AA/2)]+Sin[(AA/2)])),((Cos[AA]+Cot[(AA/2)]+2 Sin[AA])/(1+Cot[(AA/2)]))},{((3 ((Sin[AA])^2))/(1-Cos[AA]+Sin[AA])),((3 Sin[AA])/(1+Cot[(AA/2)]))}},{{(1/2) (3-Cos[AA]-(6/(1+Cot[(AA/2)]))-3 Sin[AA]),((Cos[(AA/2)] (-2+2 Cos[AA]+Sin[AA]))/(Cos[(AA/2)]+Sin[(AA/2)]))},{(1/2) (1-Cos[AA]-3 Sin[AA]),((-2+2 Cos[AA]+Sin[AA])/(1+Tan[(AA/2)]))},{-((-1+Cos[AA]+2 Sin[AA])/(1+Tan[(AA/2)])),(1/2) (1+Cos[AA]-3 Sin[AA])},{-((Cos[(AA/2)] (-1+Cos[AA]+2 Sin[AA]))/(Cos[(AA/2)]+Sin[(AA/2)])),-((Cos[AA]+Cot[(AA/2)]+2 Sin[AA])/(1+Cot[(AA/2)]))},{-((3 ((Sin[AA])^2))/(1-Cos[AA]+Sin[AA])),-((3 Sin[AA])/(1+Cot[(AA/2)]))}}},
11,
{{{0,0},{Sin[AA]+((3 Sin[AA])/(-1+2 Cos[AA]))-2 Sin[2 AA],0},{Sin[AA]-Sin[2 AA],Cos[AA] (1+((4 ((Sin[AA])^2))/(-1+2 Cos[AA])))},{-Sin[2 AA],((4 Cos[AA] ((Sin[AA])^2))/(-1+2 Cos[AA]))},{0,((-2 Cos[AA]+Cos[2 AA])/(1-2 Cos[AA]))}},{{0,0},{Sin[AA]+((3 Sin[AA])/(-1+2 Cos[AA]))-2 Sin[2 AA],0},{Sin[AA]-Sin[2 AA],-Cos[AA] (1+((4 ((Sin[AA])^2))/(-1+2 Cos[AA])))},{-Sin[2 AA],-((4 Cos[AA] ((Sin[AA])^2))/(-1+2 Cos[AA]))},{0,-((-2 Cos[AA]+Cos[2 AA])/(1-2 Cos[AA]))}},{{(2-6 Cos[AA]+(3/(-1+2 Cos[AA]))) Sin[AA],((-2 ((Cos[AA])^2)+Cos[3 AA])/(-1+2 Cos[AA]))},{(1-2 Cos[AA]) Sin[AA],((-2 ((Cos[AA])^2)+Cos[3 AA])/(-1+2 Cos[AA]))},{Sin[AA]+((3 Sin[AA])/(-1+2 Cos[AA]))-2 Sin[2 AA],-1+(3/(1-2 Cos[AA]))+2 Cos[2 AA]},{(2-4 Cos[AA]+(3/(-1+2 Cos[AA]))) Sin[AA],-1+(3/(1-2 Cos[AA]))+Cos[AA]+2 Cos[2 AA]},{(2-6 Cos[AA]+(3/(-1+2 Cos[AA]))) Sin[AA],-1+(3/(1-2 Cos[AA]))+Cos[AA]+Cos[2 AA]}},{{(2-6 Cos[AA]+(3/(-1+2 Cos[AA]))) Sin[AA],((-2 ((Cos[AA])^2)+Cos[3 AA])/(-1+2 Cos[AA]))},{(1-2 Cos[AA]) Sin[AA],((-2 ((Cos[AA])^2)+Cos[3 AA])/(-1+2 Cos[AA]))},{Sin[AA]+((3 Sin[AA])/(-1+2 Cos[AA]))-2 Sin[2 AA],0},{(2-4 Cos[AA]+(3/(-1+2 Cos[AA]))) Sin[AA],-Cos[AA]},{(2-6 Cos[AA]+(3/(-1+2 Cos[AA]))) Sin[AA],-Cos[AA]+Cos[2 AA]}},{{(((-2+4 Cos[AA]-3 Cos[2 AA]) Sin[AA])/(-1+2 Cos[AA])),((2+Cos[AA]+2 Cos[2 AA]-3 Cos[3 AA])/(2-4 Cos[AA]))},{-2 Sin[2 AA]+Sin[3 AA],((1+2 Cos[AA]-3 Cos[3 AA]+Cos[4 AA])/(1-2 Cos[AA]))},{(2-(3/(1-2 Cos[AA]))-4 Cos[AA]) Sin[AA],-2+(3/(1-2 Cos[AA]))+Cos[AA]+2 Cos[2 AA]},{(2-(3/(1-2 Cos[AA]))-4 Cos[AA]) Sin[AA],-1+(3/(1-2 Cos[AA]))+Cos[AA]+2 Cos[2 AA]},{Sin[AA]+((3 Sin[AA])/(-1+2 Cos[AA]))-2 Sin[2 AA],-1+(3/(1-2 Cos[AA]))+2 Cos[2 AA]}},{{(((-2+4 Cos[AA]-3 Cos[2 AA]) Sin[AA])/(-1+2 Cos[AA])),((2+Cos[AA]+2 Cos[2 AA]-3 Cos[3 AA])/(2-4 Cos[AA]))},{-2 Sin[2 AA]+Sin[3 AA],((1+2 Cos[AA]-3 Cos[3 AA]+Cos[4 AA])/(1-2 Cos[AA]))},{-2 Sin[2 AA]+Sin[3 AA],((2 Cos[2 AA]-3 Cos[3 AA]+Cos[4 AA])/(1-2 Cos[AA]))},{-Sin[2 AA]+Sin[3 AA],((Cos[AA]-4 Cos[3 AA] ((Sin[(AA/2)])^2))/(1-2 Cos[AA]))},{-Sin[2 AA],((4 Cos[AA] ((Sin[AA])^2))/(1-2 Cos[AA]))}},{{((3 (Sin[AA]-2 Sin[2 AA]+Sin[3 AA]))/(2-4 Cos[AA])),((Sin[AA] Sin[2 AA])/(-1+2 Cos[AA]))},{((8 Cos[AA] ((Sin[AA])^3))/(-1+2 Cos[AA])),-3 Cos[AA]+(3/(-1+2 Cos[AA]))-Cos[2 AA]+Cos[3 AA]},{-Sin[2 AA],((1-3 Cos[AA]+Cos[3 AA])/(1-2 Cos[AA]))},{-Sin[2 AA],((4 Cos[AA] ((Sin[AA])^2))/(-1+2 Cos[AA]))},{(1-2 Cos[AA]) Sin[AA],((1+Cos[2 AA]-Cos[3 AA])/(-1+2 Cos[AA]))}},{{((3 (Sin[AA]-2 Sin[2 AA]+Sin[3 AA]))/(2-4 Cos[AA])),((Sin[AA] Sin[2 AA])/(-1+2 Cos[AA]))},{((8 Cos[AA] ((Sin[AA])^3))/(-1+2 Cos[AA])),-3 Cos[AA]+(3/(-1+2 Cos[AA]))-Cos[2 AA]+Cos[3 AA]},{((8 Cos[AA] ((Sin[AA])^3))/(-1+2 Cos[AA])),-Cos[AA]-Cos[2 AA]+Cos[3 AA]},{((Sin[AA]-3 Sin[2 AA]+Sin[3 AA]+Sin[4 AA])/(1-2 Cos[AA])),-4 Cos[AA] ((Sin[AA])^2)},{(2+(3/(-1+2 Cos[AA]))) Sin[AA]-2 Sin[2 AA],-Cos[AA]}}},
12,
{{{0,1},{3 Cot[(AA/4)]-4 Sin[(AA/2)],1},{(4 Cos[(AA/4)]+Cos[((3 AA)/4)]+Cos[((5 AA)/4)]) Csc[((3 AA)/4)],1+((1+Cos[AA]+Cos[((3 AA)/2)])/(-Cos[(AA/2)]+Cos[AA]))},{(1/2) (-(4/(1+2 Cos[(AA/2)]))+((Csc[(AA/4)])^2)) Sin[AA],2+((1/(-1+Cos[(AA/2)]))+(1/((1/2)+Cos[(AA/2)]))) Cos[AA]},{0,2}},{{0,1},{3 Cot[(AA/4)]-4 Sin[(AA/2)],1},{(4 Cos[(AA/4)]+Cos[((3 AA)/4)]+Cos[((5 AA)/4)]) Csc[((3 AA)/4)],((1+Cos[(AA/2)]+Cos[((3 AA)/2)])/(Cos[(AA/2)]-Cos[AA]))},{(1/2) (-(4/(1+2 Cos[(AA/2)]))+((Csc[(AA/4)])^2)) Sin[AA],(((-1+4 Cos[(AA/2)]) Cos[AA])/(Cos[(AA/2)]-Cos[AA]))},{0,0}},{{(8 Cos[(AA/4)]+4 Cos[((3 AA)/4)]+3 Cos[((5 AA)/4)]) Csc[((3 AA)/4)],1+((1+Cos[AA]+Cos[((3 AA)/2)])/(Cos[(AA/2)]-Cos[AA]))},{(4 Cos[(AA/4)]+Cos[((3 AA)/4)]+Cos[((5 AA)/4)]) Csc[((3 AA)/4)],1+((1+Cos[AA]+Cos[((3 AA)/2)])/(Cos[(AA/2)]-Cos[AA]))},{3 Cot[(AA/4)]-4 Sin[(AA/2)],1+((2 (1+Cos[AA]+Cos[((3 AA)/2)]))/(Cos[(AA/2)]-Cos[AA]))},{3 Cot[(AA/4)]-2 Sin[(AA/2)],((1+2 Cos[(AA/2)]+3 Cos[((3 AA)/2)])/(Cos[(AA/2)]-Cos[AA]))},{(8 Cos[(AA/4)]+4 Cos[((3 AA)/4)]+3 Cos[((5 AA)/4)]) Csc[((3 AA)/4)],((1+Cos[AA]+Cos[((3 AA)/2)])/(Cos[(AA/2)]-Cos[AA]))}},{{(8 Cos[(AA/4)]+4 Cos[((3 AA)/4)]+3 Cos[((5 AA)/4)]) Csc[((3 AA)/4)],1+((1+Cos[AA]+Cos[((3 AA)/2)])/(Cos[(AA/2)]-Cos[AA]))},{(4 Cos[(AA/4)]+Cos[((3 AA)/4)]+Cos[((5 AA)/4)]) Csc[((3 AA)/4)],1+((1+Cos[AA]+Cos[((3 AA)/2)])/(Cos[(AA/2)]-Cos[AA]))},{3 Cot[(AA/4)]-4 Sin[(AA/2)],1},{3 Cot[(AA/4)]-2 Sin[(AA/2)],1+2 Cos[(AA/2)]},{(8 Cos[(AA/4)]+4 Cos[((3 AA)/4)]+3 Cos[((5 AA)/4)]) Csc[((3 AA)/4)],1+((1+Cos[(AA/2)]+Cos[((3 AA)/2)])/(Cos[(AA/2)]-Cos[AA]))}},{{(1/2) (-3 Cos[(AA/4)]-4 Cos[((3 AA)/4)]+Cos[((5 AA)/4)]) Csc[((3 AA)/4)],2+(1/(-1-2 Cos[(AA/2)]))+(1/(-1+Cos[(AA/2)]))+Cos[(AA/2)]},{(2 Cos[(AA/4)]+Cos[((3 AA)/4)]+2 Cos[((5 AA)/4)]+Cos[((7 AA)/4)]) Csc[((3 AA)/4)],((1-Cos[(AA/2)]+Cos[AA]+Cos[((3 AA)/2)]+Cos[2 AA])/(-Cos[(AA/2)]+Cos[AA]))},{0,2},{0,0},{(-Cos[(AA/4)]-2 Cos[((3 AA)/4)]) Csc[((3 AA)/4)],2+((2+Cos[(AA/2)])/(-Cos[(AA/2)]+Cos[AA]))}},{{(1/2) (-3 Cos[(AA/4)]-4 Cos[((3 AA)/4)]+Cos[((5 AA)/4)]) Csc[((3 AA)/4)],2+(1/(-1-2 Cos[(AA/2)]))+(1/(-1+Cos[(AA/2)]))+Cos[(AA/2)]},{(2 Cos[(AA/4)]+Cos[((3 AA)/4)]+2 Cos[((5 AA)/4)]+Cos[((7 AA)/4)]) Csc[((3 AA)/4)],((1-Cos[(AA/2)]+Cos[AA]+Cos[((3 AA)/2)]+Cos[2 AA])/(-Cos[(AA/2)]+Cos[AA]))},{(2 Cos[(AA/4)]+Cos[((3 AA)/4)]+2 Cos[((5 AA)/4)]+Cos[((7 AA)/4)]) Csc[((3 AA)/4)],((Cos[(AA/2)]+3 Cos[AA]+Cos[((3 AA)/2)]+Cos[2 AA])/(-Cos[(AA/2)]+Cos[AA]))},{(Cos[(AA/4)]+Cos[((3 AA)/4)]+2 (Cos[((5 AA)/4)]+Cos[((7 AA)/4)])) Csc[((3 AA)/4)],((1+3 Cos[AA]+2 Cos[2 AA])/(-Cos[(AA/2)]+Cos[AA]))},{(-2 (Cos[(AA/4)]+Cos[((3 AA)/4)])+Cos[((5 AA)/4)]) Csc[((3 AA)/4)],((1+Cos[AA]+Cos[((3 AA)/2)])/(-Cos[(AA/2)]+Cos[AA]))}},{{(1/2) (11 Cos[(AA/4)]+8 Cos[((3 AA)/4)]+7 Cos[((5 AA)/4)]+4 Cos[((7 AA)/4)]) Csc[((3 AA)/4)],6+7 Cos[(AA/2)]+(1/(1+2 Cos[(AA/2)]))+4 Cos[AA]-((Csc[(AA/4)])^2)},{(2 Cos[(AA/4)]+Cos[((3 AA)/4)]+2 Cos[((5 AA)/4)]+Cos[((7 AA)/4)]) Csc[((3 AA)/4)],((Cos[(AA/2)]+3 Cos[AA]+Cos[((3 AA)/2)]+Cos[2 AA])/(-Cos[(AA/2)]+Cos[AA]))},{2 (2 Cos[(AA/4)]+Cos[((3 AA)/4)]+2 Cos[((5 AA)/4)]+Cos[((7 AA)/4)]) Csc[((3 AA)/4)],-(1/2) (1+2 Cos[((3 AA)/2)]) ((Csc[(AA/4)])^2)},{2 (2 Cos[(AA/4)]+Cos[((3 AA)/4)]+2 Cos[((5 AA)/4)]+Cos[((7 AA)/4)]) Csc[((3 AA)/4)],8+8 Cos[(AA/2)]+4 Cos[AA]-(3/2) ((Csc[(AA/4)])^2)},{(5 Cos[(AA/4)]+4 (Cos[((3 AA)/4)]+Cos[((5 AA)/4)])+2 Cos[((7 AA)/4)]) Csc[((3 AA)/4)],6+8 Cos[(AA/2)]+(1/(1+2 Cos[(AA/2)]))+4 Cos[AA]-((Csc[(AA/4)])^2)}},{{(1/2) (11 Cos[(AA/4)]+8 Cos[((3 AA)/4)]+7 Cos[((5 AA)/4)]+4 Cos[((7 AA)/4)]) Csc[((3 AA)/4)],6+7 Cos[(AA/2)]+(1/(1+2 Cos[(AA/2)]))+4 Cos[AA]-((Csc[(AA/4)])^2)},{(2 Cos[(AA/4)]+Cos[((3 AA)/4)]+2 Cos[((5 AA)/4)]+Cos[((7 AA)/4)]) Csc[((3 AA)/4)],((Cos[(AA/2)]+3 Cos[AA]+Cos[((3 AA)/2)]+Cos[2 AA])/(-Cos[(AA/2)]+Cos[AA]))},{(2 Cos[(AA/4)]+Cos[((3 AA)/4)]+2 Cos[((5 AA)/4)]+Cos[((7 AA)/4)]) Csc[((3 AA)/4)],((1-Cos[(AA/2)]+Cos[AA]+Cos[((3 AA)/2)]+Cos[2 AA])/(-Cos[(AA/2)]+Cos[AA]))},{(3 Cos[(AA/4)]+Cos[((3 AA)/4)]+2 Cos[((5 AA)/4)]) Csc[((3 AA)/4)],((Cos[AA]+2 Cos[((3 AA)/2)])/(-Cos[(AA/2)]+Cos[AA]))},{(6 Cos[(AA/4)]+4 Cos[((3 AA)/4)]+3 Cos[((5 AA)/4)]+2 Cos[((7 AA)/4)]) Csc[((3 AA)/4)],((3 Cos[AA]+Cos[((3 AA)/2)]+2 Cos[2 AA])/(-Cos[(AA/2)]+Cos[AA]))}}},
13,
{{{(1/2) (-3+3 Cos[AA]+Sin[AA]),(1/2) (1-Cos[AA]+3 Sin[AA])},{0,1},{0,0},{-1,0},{-1+2 Cos[AA],2 Sin[AA]}},{{(1/2) (-3+3 Cos[AA]+Sin[AA]),(1/2) (1-Cos[AA]+3 Sin[AA])},{-3+3 Cos[AA]+Sin[AA],-Cos[AA]+3 Sin[AA]},{3 (-1+Cos[AA]),3 Sin[AA]},{-3+2 Cos[AA],2 Sin[AA]},{-1+2 Cos[AA],2 Sin[AA]}},{{(1/2) (-3+3 Cos[AA]+Sin[AA]),(1/2) (1-Cos[AA]+3 Sin[AA])},{0,1},{Sin[AA],1-Cos[AA]},{Cos[AA]+Sin[AA],1-Cos[AA]+Sin[AA]},{-2+Cos[AA]+Sin[AA],1-Cos[AA]+Sin[AA]}},{{(1/2) (-3+3 Cos[AA]+Sin[AA]),(1/2) (1-Cos[AA]+3 Sin[AA])},{-3+3 Cos[AA]+Sin[AA],-Cos[AA]+3 Sin[AA]},{-3+3 Cos[AA]+Sin[AA],1-Cos[AA]+3 Sin[AA]},{-2+3 Cos[AA]+Sin[AA],1-Cos[AA]+3 Sin[AA]},{-2+Cos[AA]+Sin[AA],1-Cos[AA]+Sin[AA]}},{{(1/2) (1-Cos[AA]+3 Sin[AA]),(1/2) (3-3 Cos[AA]-Sin[AA])},{1,0},{0,0},{0,1},{2 Sin[AA],1-2 Cos[AA]}},{{(1/2) (1-Cos[AA]+3 Sin[AA]),(1/2) (3-3 Cos[AA]-Sin[AA])},{-Cos[AA]+3 Sin[AA],3-3 Cos[AA]-Sin[AA]},{3 Sin[AA],-3 (-1+Cos[AA])},{2 Sin[AA],3-2 Cos[AA]},{2 Sin[AA],1-2 Cos[AA]}},{{(1/2) (1-Cos[AA]+3 Sin[AA]),(1/2) (3-3 Cos[AA]-Sin[AA])},{1,0},{1-Cos[AA],-Sin[AA]},{1-Cos[AA]+Sin[AA],-Cos[AA]-Sin[AA]},{1-Cos[AA]+Sin[AA],2-Cos[AA]-Sin[AA]}},{{(1/2) (1-Cos[AA]+3 Sin[AA]),(1/2) (3-3 Cos[AA]-Sin[AA])},{-Cos[AA]+3 Sin[AA],3-3 Cos[AA]-Sin[AA]},{1-Cos[AA]+3 Sin[AA],3-3 Cos[AA]-Sin[AA]},{1-Cos[AA]+3 Sin[AA],2-3 Cos[AA]-Sin[AA]},{1-Cos[AA]+Sin[AA],2-Cos[AA]-Sin[AA]}}},
14,
{{{(1/8) (-3+(Sqrt[57])),Root[-1568-71 ((#1)^2)+16 ((#1)^4)&,2]},{(1/8) (-9+3 (Sqrt[57])),Root[-1152+273 ((#1)^2)+16 ((#1)^4)&,2]},{1,0},{0,0},{0,Root[-392+25 ((#1)^2)+4 ((#1)^4)&,2]}},{{(1/8) (3-(Sqrt[57])),Root[-1568-71 ((#1)^2)+16 ((#1)^4)&,2]},{(1/8) (9-3 (Sqrt[57])),Root[-1152+273 ((#1)^2)+16 ((#1)^4)&,2]},{-1,0},{0,0},{0,Root[-392+25 ((#1)^2)+4 ((#1)^4)&,2]}},{{(1/4) (1+(Sqrt[57])),Root[-32+((#1)^2)+4 ((#1)^4)&,1]},{1,0},{(1/8) (-9+3 (Sqrt[57])),Root[-1152+273 ((#1)^2)+16 ((#1)^4)&,2]},{(1/8) (-1+3 (Sqrt[57])),Root[-1152+273 ((#1)^2)+16 ((#1)^4)&,2]},{(1/8) (-1+3 (Sqrt[57])),Root[-8+((#1)^2)+16 ((#1)^4)&,1]}},{{(1/2) (-1+(Sqrt[57])),Root[-32+((#1)^2)+4 ((#1)^4)&,1]},{(1/4) (-5+3 (Sqrt[57])),0},{(1/8) (7+3 (Sqrt[57])),Root[-1152+273 ((#1)^2)+16 ((#1)^4)&,2]},{(1/8) (-1+3 (Sqrt[57])),Root[-1152+273 ((#1)^2)+16 ((#1)^4)&,2]},{(1/8) (-1+3 (Sqrt[57])),Root[-8+((#1)^2)+16 ((#1)^4)&,1]}},{{(1/8) (7+3 (Sqrt[57])),Root[-1152+273 ((#1)^2)+16 ((#1)^4)&,2]},{(1/8) (-9+3 (Sqrt[57])),Root[-1152+273 ((#1)^2)+16 ((#1)^4)&,2]},{(1/8) (-3+(Sqrt[57])),Root[-1568-71 ((#1)^2)+16 ((#1)^4)&,2]},{(1/4) (-3+(Sqrt[57])),Root[-72-15 ((#1)^2)+((#1)^4)&,2]},{(1/16) (31+3 (Sqrt[57])),Root[-23328+2457 ((#1)^2)+64 ((#1)^4)&,2]}},{{-1,0},{1,0},{(1/4) (1+(Sqrt[57])),Root[-32+((#1)^2)+4 ((#1)^4)&,1]},{(1/8) (5+(Sqrt[57])),Root[-648+9 ((#1)^2)+16 ((#1)^4)&,1]},{(3/16) (-11+(Sqrt[57])),Root[-288+273 ((#1)^2)+64 ((#1)^4)&,1]}}},
15,{{{2-(Sqrt[3]),-17-6 (Sqrt[3])},{6-(Sqrt[3]),-17-6 (Sqrt[3])},{3 (2+(Sqrt[3])),-13-6 (Sqrt[3])},{6+(Sqrt[3]),-11-6 (Sqrt[3])},{2-(Sqrt[3]),-13-6 (Sqrt[3])}},{{-(Sqrt[3]),-13-4 (Sqrt[3])},{(Sqrt[3]),-11-4 (Sqrt[3])},{8+(Sqrt[3]),-11-4 (Sqrt[3])},{6+(Sqrt[3]),-11-6 (Sqrt[3])},{2-(Sqrt[3]),-13-6 (Sqrt[3])}},{{6+(Sqrt[3]),-11-6 (Sqrt[3])},{8+(Sqrt[3]),-11-4 (Sqrt[3])},{8+5 (Sqrt[3]),-7-4 (Sqrt[3])},{8+5 (Sqrt[3]),-11-4 (Sqrt[3])},{3 (2+(Sqrt[3])),-13-6 (Sqrt[3])}},{{-(Sqrt[3]),-13-4 (Sqrt[3])},{-2-(Sqrt[3]),-13-2 (Sqrt[3])},{-2-(Sqrt[3]),-5-2 (Sqrt[3])},{-2+(Sqrt[3]),-7-2 (Sqrt[3])},{(Sqrt[3]),-11-4 (Sqrt[3])}},{{4+(Sqrt[3]),-11-4 (Sqrt[3])},{4+(Sqrt[3]),-7-4 (Sqrt[3])},{(Sqrt[3]),-7},{-2+(Sqrt[3]),-7-2 (Sqrt[3])},{(Sqrt[3]),-11-4 (Sqrt[3])}},{{-2+(Sqrt[3]),-7-2 (Sqrt[3])},{(Sqrt[3]),-7},{(Sqrt[3]),1},{-(Sqrt[3]),-1},{-2-(Sqrt[3]),-5-2 (Sqrt[3])}},{{-2+(Sqrt[3]),17+6 (Sqrt[3])},{-6+(Sqrt[3]),17+6 (Sqrt[3])},{-3 (2+(Sqrt[3])),13+6 (Sqrt[3])},{-6-(Sqrt[3]),11+6 (Sqrt[3])},{-2+(Sqrt[3]),13+6 (Sqrt[3])}},{{(Sqrt[3]),13+4 (Sqrt[3])},{-(Sqrt[3]),11+4 (Sqrt[3])},{-8-(Sqrt[3]),11+4 (Sqrt[3])},{-6-(Sqrt[3]),11+6 (Sqrt[3])},{-2+(Sqrt[3]),13+6 (Sqrt[3])}},{{-6-(Sqrt[3]),11+6 (Sqrt[3])},{-8-(Sqrt[3]),11+4 (Sqrt[3])},{-8-5 (Sqrt[3]),7+4 (Sqrt[3])},{-8-5 (Sqrt[3]),11+4 (Sqrt[3])},{-3 (2+(Sqrt[3])),13+6 (Sqrt[3])}},{{(Sqrt[3]),13+4 (Sqrt[3])},{2+(Sqrt[3]),13+2 (Sqrt[3])},{2+(Sqrt[3]),5+2 (Sqrt[3])},{2-(Sqrt[3]),7+2 (Sqrt[3])},{-(Sqrt[3]),11+4 (Sqrt[3])}},{{-4-(Sqrt[3]),11+4 (Sqrt[3])},{-4-(Sqrt[3]),7+4 (Sqrt[3])},{-(Sqrt[3]),7},{2-(Sqrt[3]),7+2 (Sqrt[3])},{-(Sqrt[3]),11+4 (Sqrt[3])}},{{2-(Sqrt[3]),7+2 (Sqrt[3])},{-(Sqrt[3]),7},{-(Sqrt[3]),-1},{(Sqrt[3]),1},{2+(Sqrt[3]),5+2 (Sqrt[3])}}} /8];

Manipulate

Manipulate[
If[oldtype ≠ type,
 oldtype = type;
AA= {1.571,1.571,0,1.571,2.356,2.094,2.689,1.571,0,1.571,2.113,2.18,2.356,0,0}[[type]];
BB= {1.571,1.571,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]];
b= {1,1,0.5,1.5,0.5,0,0,0,1.573,0,0,0,0,0,0}[[type]];
c= {1,0,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]];
e= {1,1,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]]   ];
With[{pentset=  motif[type,AA,BB,b,c,e], off=offset[type,AA,BB,b,c,e]}, With[{pents = Flatten[Table[pentset +Table[x off[[1]] +y off[[2]], {Length[pentset]},{5}],{x,-v1,v1},{y,-v2,v2}],2]},
Graphics[{EdgeForm[Thick],color,Polygon/@pents},PlotRange-> {{-range,range},{-range,range}}, ImageSize-> {450,450}]]],
"tiling type",
{{type, 8, ""},Range[1,15]},
{{oldtype, 8},ControlType->None },
" ",
"angles and sides",
{{AA, 1.571},{0,0,0,0,(π/2),(π/3),2.237035759287412`,0,0,0.927296`,1.945531`,1.722769`,(π/2),0,0,0}[[type]],{π,π,0,π,π,π,π,π,0,2.214297`,2.280208`,2.636232`,π,0,0}[[type]],  ImageSize-> Tiny, Enabled -> enables[[1,type]]},
{{BB,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]],{π,π,0,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]],  ImageSize-> Tiny, Enabled -> enables[[2,type]]},
{{b, 0},{0,0,0,0,0,0,0,0,(Sqrt[2]),0,0,0,0,0,0}[[type]],{2,2,1,3,1,0,0,0,(Sqrt[3]),0,0,0,0,0,0,0}[[type]], ImageSize-> Tiny, Enabled -> enables[[3,type]]},
{{c, 0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]],{2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]], ImageSize-> Tiny, Enabled -> enables[[4,type]]},
{{e, 0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]],{2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]],  ImageSize-> Tiny, Enabled -> enables[[5,type]]},
" ",
"repetition vectors",
{{v1,2},0,5,1, ImageSize-> Tiny},
{{v2,2},0,5,1, ImageSize-> Tiny},
" ",
"plot range",
{{range,4, ""},1,9, ImageSize-> Tiny},
" ",
"color",
{{color,Cyan, ""},Pink, ImageSize-> Tiny},
ControlPlacement->Left, TrackedSymbols:>{AA,BB, b,c,e,type, v1, v2, range, color}, SaveDefinitions-> True,AutorunSequencing->{1,3,8,9,10,11}]

Figure

bug(299169): There is something wrong with the Demonstrations code for tilings type 1 and 2.  Unless squares are the new
pentagons

Change the values of a, b, and c for the first and second indices to match those on W|A

GraphicsGrid[Partition[Table[Module[{v1=5,v2=5,
AA= {2.0944,2.0944,0,1.571,2.356,2.094,2.689,1.571,0,1.571,2.113,2.18,2.356,0,0}[[type]],
BB= {2.0944,1.8326,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]],
b= {.6,.9,0.5,1.5,0.5,0,0,0,1.573,0,0,0,0,0,0}[[type]],
c= {.7,0,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]],
e= {.8,1.2,0,0,0,0,0,0,0,0,0,0,0,0,0}[[type]]},
With[{pentset=  motif[type,AA,BB,b,c,e], off=offset[type,AA,BB,b,c,e]}, With[{pents = Flatten[Table[pentset +Table[x off[[1]] +y off[[2]], {Length[pentset]},{5}],{x,-v1,v1},{y,-v2,v2}],2]},
Graphics[{EdgeForm[Thin],White,Polygon/@pents},PlotRange-> 4,PlotLabel->TextCell[Style["           type "<>ToString[type]<>"           ",Italic],Background->White]]]]],{type,15}],5,5,1,{}],ImageSize->500,Spacings->{Automatic,50}]