~ ~ ~ ~ ~ OCTAHEDRON 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=vector(u*cos([2*m])*sin([2*n])-(u*cos([2*p])*sin([2*q])),u*v*sin([2*m])*sin([2*n])-(u*v*sin([2*p])*sin([2*q])),u*cos([2*n])-(u*cos([2*q])))

D=vector(-(2*V_5*v),V_3*sin([2*pi*u]),V_3*cos([2*pi*u])),E=vector(V_5,V_4*V_5,0),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=0.55,V_2=0.02,V_3=0.007,V_4=plusorminus(1),V_5=1/sqrt(2)

S_1=set(0),S_2=set(pi/4),S_3=set(-pi/8,pi/8),S_4=set(0,pi/4,2*pi/4,3*pi/4)

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vector(x,y,z)=V_1*A

vector(x,y,z)=V_2*A+B,in(p,S_3),in(q,S_4)

vector(x,y,z)=I*V_4*C+I*V_4*B,in(m,S_3),in(n,S_2),in(p,S_1),in(q,S_1),in(g,S_1),in(h,S_1),in(b,S_4)

vector(x,y,z)=I*D+I*E,in(g,S_3),in(h,S_2),in(b,S_4)

Graph of the formula

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