Cube In A Dodecahedron?
How many different cubes can be formed, if any, from the vertices of a dodecahedron?
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1 solution
Relevant wiki: Platonic Solids
5 cubes can be formed.
Here is an illustration of one:
You'll notice that each of the 12 faces of the dodecahedron contains one edge of the resulting cube.
And, by symmetry, you can pick any pair of vertices on a given pentagonal face that aren't adjacent (there are 5 such pairs) and use that as the edge of a similarly sized cube, resulting in 5 possible ways to construct a cube.