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There are only five regular convex polyhedra. ... There are indeed only five regular (convex) polyhedra. And the fact was known to the ancient Greeks. Another term for the regular (convex) polyhedra is Platonic bodies. The fact is very well known and there is a great variety of different proofs to choose from.
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www.cut-the-knot.org/do_you_know/polyhedra.shtml
www.cut-the-knot.org/do_you_know/polyhedra.shtml
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Regular polyhedron - Wikipedia, the free encyclopedia
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A regular polyhedron is a polyhedron whose faces are congruent regular polygons which are assembled in the same way around each vertex. A regular polyhedron is highly symmetrical, being all of edge-...
en.wikipedia.org/wiki/Regular_polyhedron
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Platonic solid - Wikipedia, the free encyclopedia
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In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same num...
en.wikipedia.org/wiki/Platonic_solid
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Science Fair Project: Making the five regular solids (out of toothpicks or paper or something else) may make a good science fair project. Addendum #5 (below) shows models for the five regular polyhedra.
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www.jimloy.com/geometry/hedra.htm
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The five regular polyhedra were discovered by the ancient Greeks. The Pythagoreans knew of the tetrahedron, the cube, and the dodecahedron; the mathematician Theaetetus added the octahedron and the icosahedron. These shapes are also called the Platonic solids, after the ancient Greek philosopher Plato;
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www.enchantedlearning.com/math/geometry/solids/
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It is apparent from the Table that for all five regular polyhedra ... We'll see below that this equations actually holds for all convex polyhedra. Given m and n the above three equations determine f, e, and v uniquely, and so there are only five possible regular polyhedra.
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www.math.utah.edu/~pa/math/polyhedra/polyhedra.html
www.math.utah.edu/~pa/math/polyhedra/polyhedra.html
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The additional regular polyhedra won't be discussed in this report, but information about them may be found in the Bibliography. Here is a summary of the five convex regular polyhedra: Number Number Number Reg.
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www.iit.edu/~smile/ma8606.html
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also known as Platonic Solids ... There are just five platonic solids. ... Return to Polyhedra page.
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mathforum.org/sum95/math_and/poly/reg_polyhedra.html
mathforum.org/sum95/math_and/poly/reg_polyhedra.html
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And that makes five regular polyhedra. What about the regular hexagon, that is, the six-sided figure? Well, its interior angles are 120°, so if we fit three of them together at a vertex the angles sum to precisely 360°, and therefore they lie flat, just like four squares (or six equilateral triangles) would do.
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www.mathacademy.com/pr/prime/articles/platsol/index.asp
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