Questions related to polyhedra and their properties.

learn more… | top users | synonyms

4
votes
2answers
387 views

Which unfolding of an icosahedron has the least number of edges to be glued?

Does every unfolding of an icosahedron has the same number of edges to be glued to construct it back to the solid? If yes, what are those numbers for Platonic solids? If no, which unfoldings have the ...
20
votes
3answers
9k views

Why are there 12 pentagons and 20 hexagons on a soccer ball?

Edge-attaching many hexagons results in a plane. Edge-attaching pentagons yields a dodecahedron. Is there some insight into why the alternation of pentagons and hexagons yields an approximated ...
2
votes
1answer
391 views

Find the Polyhedron Enclosed by Multiple Faces

I have two faces ($S_1$ and $S_2$), each bounded by a series of Vertex $V$. These two faces may or may not intersect. In addition to that there are two vertical faces $S_3$ and $S_4$, that connect ...
6
votes
2answers
3k views

Tetrahedron inside a sphere

What's the largest regular tetrahedron (side length x) you can fit inside a sphere with a radius of one?
4
votes
3answers
16k views

Height of a tetrahedron

How do I calculate: The height of a regular tetrahedron, side length 1. Just to be completely clear, by height I mean if you placed the shape on a table, how high up would the highest point be from ...
4
votes
1answer
302 views

Tetrahedron volume

How to calculate volume of tetrahedron given lengths of all it's edges?
11
votes
1answer
350 views

What property of certain regular polygons allows them to be faces of the Platonic Solids?

It appears to me that only Triangles, Squares, and Pentagons are able to "tessellate" (is that the proper word in this context?) to become regular 3D convex polytopes. What property of those regular ...