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kengrThis is likely not anything new to the math geeks, but I thought it might be of interest to the rest of you.
Consider the 5 regular polyhedra (best known from gaming dice these days)
tetrahedron
4 sides, 4 points, and 6 edges.
hexahedron (cube)
6 sides, 8 points, and 12 edges
octahedron
8 sides, 6 points, and 12 edges
dodecahedron
12 sides, 20 points, and 30 edges
icosahedron
20 sides, 12 points, and 30 edges
so the hexahedron and octahedron are a symmetry pair (just swap edges and points and they are the "same"). Ditto for the edodecahedron and the icosahedron.
And the tetrahedron is its own "symmetry twin".
This sort of thing, but in higher dimensions is behind the way the universe works. High end physics theory turns out to be symmetries in those higher dimensions.
Consider the 5 regular polyhedra (best known from gaming dice these days)
tetrahedron
4 sides, 4 points, and 6 edges.
hexahedron (cube)
6 sides, 8 points, and 12 edges
octahedron
8 sides, 6 points, and 12 edges
dodecahedron
12 sides, 20 points, and 30 edges
icosahedron
20 sides, 12 points, and 30 edges
so the hexahedron and octahedron are a symmetry pair (just swap edges and points and they are the "same"). Ditto for the edodecahedron and the icosahedron.
And the tetrahedron is its own "symmetry twin".
This sort of thing, but in higher dimensions is behind the way the universe works. High end physics theory turns out to be symmetries in those higher dimensions.
