1
vote
0answers
77 views

method to construct platonic solids from the circumscribed sphere [closed]

I am trying to find a geometrical method of building the platonic solids starting from the circumscribed sphere. I do have a class of generative 3d modeling where we create 3d object programmatically ...
24
votes
3answers
887 views

About the ratio of the areas of a convex pentagon and the inner pentagon made by the five diagonals

Question : Letting $S{^\prime}$ be the area of the inner pentagon made by the five diagonals of a convex pentagon whose area is $S$, then find the max of $\frac{S^\prime}{S}$. ...
3
votes
0answers
128 views

Tetrahedra passing through a hole

Assume a plane $P\subset\mathbb R^3$ has a hole $H$, and that the hole is topologically a compact disc. Being so, $P\setminus H$ does not separate the space. A regular tetrahedron $\sigma^3$ (of ...
8
votes
3answers
492 views

On maximal regular polyhedra inscribed in a regular polyhedron

Let T, C, O, D, or I be regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron, respectively. Suppose that the outer polyhedron have edge-length 1. For example, it's easy to prove that ...