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Tutorial - How to make dodecahedron pot

By frei on 02 Jun 18:20 1 answer 3035 views 0 comments

Dodecahedron pot

What we should know about dodecahedron and other platonic solids.
http://en.wikipedia.org/wiki/Dodecahedron
http://en.wikipedia.org/wiki/Platonic_solid
http://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol

Equations in model:

{p,q} is a Schläfli symbol, for dodecahedron {5,3}

p=5 //the number of parties at the brink
q=3 //the number of edges adjacent to the vertices

a=51 //lenght of rib

sintheta=(cos (180/q)/sin (180/p)) //separate variable angle to simplify the formula of theta

theta=2*asin (sintheta) //dihedral angle
epsilon=2*sin (36) //constant need to equal radius of inscribed sphere
phi=2*cos (36) // phi is "golden ratio" also is (1+sqrt(5))/2. 36=pi/5=180/5,
rad=a*0.5*phi*phi/epsilon // radius of inscribed sphere which is tangent to each face at the center of the face.

Added images

Square

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