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A Platonic solid is a solid for which
The Five Convex Regular Polyhedra (Platonic solids) -- thanks Wikipedia! | ||||
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Tetrahedron | Hexahedron or Cube |
Octahedron | Dodecahedron | Icosahedron |
The Platonic solids allow us to make "flat spheres" (sort of!):
"The six spheres each corresponded to one of the planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn). The solids were ordered with the innermost being the octahedron, followed by the icosahedron, dodecahedron, tetrahedron, and finally the cube. In this way the structure of the solar system and the distance relationships between the planets was dictated by the Platonic solids."
And then Uranus was discovered, and there was not sixth Platonic solid. And so science evolves....
These are some higher quality images than my scans:
From the October 7th, 2011 New York Times
"An array of viruses. (a) The helical virus of rabies. (b) The segmented helical virus of influenza. (c) A bacteriophage with an icosahedral head and helical tail. (d) An enveloped icosahedral herpes simplex virus. (e) The unenveloped polio virus. (f) The icosahedral human immunodeficiency virus with spikes on its envelope."
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# of Vertices | Edges | Faces | faces at each vertex | sides at each face | |
Tetrahedron | |||||
Cube | |||||
Octahedron | |||||
Dodecahedron | |||||
Icosahedron |
What conclusions can we draw from this data? Is there a pattern? (Of course there is!:) The pattern leads to the concept of "Duality":
"In the Hindu tradition, the icosahedron represents purusha, the male, spiritual principle, and generates the dodecahedron, representing prakriti, the female, material principle." |