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Topic: Regular polyhedrons (Read 533 times) |
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Ghost Sniper
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Regular polyhedrons
« on: Nov 11th, 2007, 12:34pm » |
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Prove, mathematically, that there exist only 5 regular polyhedrons.
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towr
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Re: Regular polyhedrons
« Reply #1 on: Nov 11th, 2007, 12:54pm » |
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We know 5, and there can't be more; therefore there are only 5 
Well ok:
There can't be more, because we can only use regular triangles, squares, and pentagons. You always need at least 3 polygons to meet at a vertex, and you can't have more than 5 triangles, 3 squares or 3 pentagons meet at a vertex. So at most 3+1+1=5.
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| « Last Edit: Nov 11th, 2007, 12:54pm by towr » |
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ecoist
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Re: Regular polyhedrons
« Reply #2 on: Nov 12th, 2007, 9:41am » |
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A fun one is determing all convex deltahedra! A convex deltahedron is a convex polyhedron, all of whose faces are equilateral triangles. Can you imagine what my favorite, with 14 faces, looks like?
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towr
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Re: Regular polyhedrons
« Reply #3 on: Nov 12th, 2007, 10:09am » |
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on Nov 12th, 2007, 9:41am, ecoist wrote:| A fun one is determing all convex deltahedra! A convex deltahedron is a convex polyhedron, all of whose faces are equilateral triangles. |
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Aren't there infinitely many? Or is it disallowed for (adjacent) triangles to lie in the same plane?
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Grimbal
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Re: Regular polyhedrons
« Reply #4 on: Nov 13th, 2007, 12:43am » |
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on Nov 12th, 2007, 9:41am, ecoist wrote:| Can you imagine what my favorite, with 14 faces, looks like? |
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If it has 14 faces, there is only one, the triaugmented triangular prism.
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