by Fredfredburger » Wed Mar 06, 2013 9:21 pm
For a dodecahedron with edge e the midradius can be calculated with
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where phi denotes the golden ratio.
In general, for the Platonic solids with Schäfli symbol [unparseable or potentially dangerous latex formula] and edge e, the midradius can be found with the formula
[unparseable or potentially dangerous latex formula]
Where h takes on values of 4, 6, 6, 10, and 10 for the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron respectively.
The other two that I suggest you know are the circumradius and inradius. Theta denotes the dihedral angle.
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
MIT '17