Although this question does not seem to be much of physics, but still it may be of interest for lots of physicist around
There are 5 platonic solids, the tetrahedron (4 vertices, 4 triangular faces, 6 edges), the cube (8 vertices, 6 square faces, 12 edges), the octahedron (6 vertices, 8 triangular faces, 12 edges), the dodecahedron (20 vertices, 12 pentagonal faces, 30 edges) and the icosahedron (12 vertices, 20 triangular faces, 30 edges). Consider open models of these solids with wire edges connecting the vertices. Suppose each wire has unit resistance. For each case find the total resistance between a pair of adjacent vertices. Express each answer as a rational number.
Hint: The answers can be found by brute force but there is a way to use symmetry.
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