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Regular polytope
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===Convex polygons and polyhedra=== The earliest surviving mathematical treatment of regular polygons and polyhedra comes to us from [[ancient Greece|ancient Greek]] mathematicians. The five [[Platonic solid]]s were known to them. [[Pythagoras]] knew of at least three of them and [[Theaetetus (mathematician)|Theaetetus]] (c. 417 BC β 369 BC) described all five. Later, [[Euclid]] wrote a systematic study of mathematics, publishing it under the title ''[[Euclid's Elements|Elements]]'', which built up a logical theory of geometry and [[number theory]]. His work concluded with mathematical descriptions of the five [[Platonic solid]]s. :{| class="wikitable" |- |colspan=5 align=center|'''[[Platonic solid]]s''' |- |align=center|[[Image:Tetrahedron.svg|75px]] |align=center|[[Image:Hexahedron.svg|75px]] |align=center|[[Image:Octahedron.svg|75px]] |align=center|[[Image:POV-Ray-Dodecahedron.svg|75px]] |align=center|[[Image:Icosahedron.svg|75px]] |- |[[Tetrahedron]]||[[Cube]]||[[Octahedron]]||[[Dodecahedron]]||[[Icosahedron]] |}
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