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 ...
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 ...
What's the largest regular tetrahedron (having side length $x$) you can fit inside a sphere with a unit radius?
How do I calculate the height of a regular tetrahedron having 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 ...
How to calculate volume of tetrahedron given lengths of all it's edges?
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 ...