~ ~ ~ ~ ~ DODECAHEDRON by J. Snuszka ~ ~ ~ ~ ~

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A=vector(cos([2*pi*v])*sin([2*pi*u]),sin([2*pi*v])*sin([2*pi*u]),cos([2*pi*u])),B=vector(cos([2*p])*sin([2*q]),sin([2*p])*sin([2*q]),cos([2*q])),C_1=vector(u*cos([2*m])*sin([2*n])-(V_7*u*cos([2*p])*sin([2*q])),u*v*sin([2*m])*sin([2*n])-(V_7*u*v*sin([2*p])*sin([2*q])),u*cos([2*n])-(V_7*u*cos([2*q])))

C_2=vector(u*cos([2*m])*sin([2*n])-(V_7*u*cos([2*p])*sin([2*q])),u*sin([2*m])*sin([2*n])-(V_7*u*sin([2*p])*sin([2*q])),u*v*cos([2*n])-(V_7*u*v*cos([2*q]))),C_3=vector(u*v*cos([2*m])*sin([2*n])-(V_7*u*v*cos([2*p])*sin([2*q])),u*sin([2*m])*sin([2*n])-(V_7*u*sin([2*p])*sin([2*q])),u*cos([2*n])-(V_7*u*cos([2*q])))

D_1=vector(V_3*sin([2*pi*u]),V_3*cos([2*pi*u]),V_5*v),D_2=vector(V_3*sin([2*pi*u]),V_5*v,V_3*cos([2*pi*u])),D_3=vector(V_5*v,V_3*sin([2*pi*u]),V_3*cos([2*pi*u])),I=matrix(3,3,a*X^2+M,a*X*Y-(N*Z),a*X*Z+N*Y,a*X*Y+N*Z,a*Y^2+M,a*Y*Z-(N*X),a*X*Z-(N*Y),a*Y*Z+N*X,a*Z^2+M)

a=1-cos([2*b]),X=cos([2*g])*sin([2*h]),Y=sin([2*g])*sin([2*h]),Z=cos([2*h]),M=cos([2*b]),N=sin([2*b])

V_1=0.65,V_2=0.02,V_3=0.007,V_4=plusorminus(1),V_5=4/(sqrt(15)+sqrt(3)),V_6=asin([2/(sqrt(15)+sqrt(3))]),V_7=cos([asin([V_5/(2*sin(pi/5))])]),V_8=asin([2/sqrt(10+2*sqrt(5))])

S_1=set(0),S_2=set(pi/4),S_3=set(-pi/4,pi/4),S_4=set(0,pi/5,2*pi/5,3*pi/5,4*pi/5),S_6=set(-pi/4),S_7=set(2*pi/5,3*pi/5,4*pi/5),S_8=set(0,pi/3,2*pi/3),S_9=set(V_6/2),S_10=set(V_8/2)

S_11=set(-V_8/2),S_12=set(pi/4+V_6/2,pi/4-V_6/2),S_13=set(pi/2),S_14=set(pi/4+V_8/2),S_15=set(pi/4-V_8/2),S_16=set(pi/4+V_6/2),S_17=set(V_6)

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vector(x,y,z)=V_1*I*A,in(g,S_2),in(h,S_2),in(b,S_17)

vector(x,y,z)=V_2*A+I*V_4*B,in(p,S_1),in(q,S_12),in(g,S_1),in(h,S_12),in(b,S_8)

vector(x,y,z)=V_2*A+I*V_4*B,in(p,S_3),in(q,S_9),in(g,S_3),in(h,S_9),in(b,S_8)

vector(x,y,z)=V_2*A+I*V_4*B,in(p,S_12),in(q,S_2),in(g,S_12),in(h,S_2),in(b,S_8)

vector(x,y,z)=I*V_4*D_1+I*V_4*B,in(p,S_1),in(q,S_16),in(g,S_1),in(h,S_12),in(b,S_8)

vector(x,y,z)=I*V_4*D_2+I*V_4*B,in(p,S_6),in(q,S_9),in(g,S_3),in(h,S_9),in(b,S_8)

vector(x,y,z)=I*V_4*D_3+I*V_4*B,in(p,S_16),in(q,S_2),in(g,S_12),in(h,S_2),in(b,S_8)

vector(x,y,z)=I*V_4*C_1+V_4*V_7*B,in(m,S_3),in(n,S_9),in(p,S_1),in(q,S_10),in(g,S_1),in(h,S_10),in(b,S_4)

vector(x,y,z)=I*V_4*C_1+V_4*V_7*B,in(m,S_3),in(n,S_9),in(p,S_13),in(q,S_10),in(g,S_13),in(h,S_10),in(b,S_4)

vector(x,y,z)=I*V_4*C_2+V_4*V_7*B,in(m,S_1),in(n,S_12),in(p,S_10),in(q,S_2),in(g,S_10),in(h,S_2),in(b,S_4)

vector(x,y,z)=I*V_4*C_2+V_4*V_7*B,in(m,S_1),in(n,S_12),in(p,S_11),in(q,S_2),in(g,S_11),in(h,S_2),in(b,S_4)

vector(x,y,z)=I*V_4*C_3+V_4*V_7*B,in(m,S_12),in(n,S_2),in(p,S_2),in(q,S_14),in(g,S_2),in(h,S_14),in(b,S_4)

vector(x,y,z)=I*V_4*C_3+V_4*V_7*B,in(m,S_12),in(n,S_2),in(p,S_2),in(q,S_15),in(g,S_2),in(h,S_15),in(b,S_4)

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