2
votes
3answers
1k views

Given a tetrahedron, how to find the outward surface normals for each side?

Say I have a triangle in $3$D space. I can get the surface normal by calculating the vector cross product of two of the edges. But, lets say I make this a tetrahedron. How can I work out the outward ...
1
vote
1answer
68 views

Determine if two polyhedrals are the same shape and if so, map their vertices

I have a polyhedron and want to determine whether it is combinatorially equivalent to another polyhedron. I know how many faces comprise each polyhedron and for each face, I know all of its vertices, ...
7
votes
2answers
263 views

Number of distinct nets of dual polyhedra

There are 11 non-congruent nets of a cube as well as 11 distinct nets of an octahedron. Both a dodecahedron and an icosahedron have 43380 distinct nets. Is it true that any pair of dual convex ...