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Some Solid Connections, Page 4: The Icosadodecahedron
Taking this investigation to the next pair of dual platonic solids, here is the bisected-edge truncation of the icosahedron:
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The bisected-edge truncation of the Dodecahedron:
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Similar to the case above (with the cube and octahedron), the bisected-edge truncations of the icosahedron and dodecahedron produce the same solid: the icosidodecahedron.
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Therefore, it can be seen the icosahedron and dodecahedron are duals:
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Now, the symmetry of the the spherical arcs from the icosahedron, dodecahedron, and the icosidodecahedron mapped on the same sphere:
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