- Archimedean solid
In

geometry an**Archimedean solid**is a highly symmetric, semi-regular convexpolyhedron composed of two or more types ofregular polygon s meeting in identical vertices. They are distinct from thePlatonic solid s, which are composed of only one type of polygon meeting in identical vertices, and from theJohnson solid s, whose regular polygonal faces do not meet in identical vertices. The symmetry of the Archimedean solids excludes the members of thedihedral group , the prisms andantiprism s. The**Archimedean solids**can all be made viaWythoff construction s from thePlatonic solids with tetrahedral, octahedral andicosahedral symmetry . See Convex uniform polyhedron.**Origin of name**The Archimedean solids take their name from

Archimedes , who discussed them in a now-lost work. During theRenaissance ,artist s andmathematician s valued "pure forms" and rediscovered all of these forms. This search was completed around1620 byJohannes Kepler , who defined prisms,antiprisms , and the non-convex solids known as theKepler-Poinsot polyhedra .**Classification**There are 13 Archimedean solids (15 if the

mirror image s of two enantiomorphs, see below, are counted separately). Here the "vertex configuration" refers to the type of regular polygons that meet at any given vertex. For example, avertex configuration of (4,6,8) means that a square,hexagon , andoctagon meet at a vertex (with the order taken to be clockwise around the vertex).The number of vertices is 720° divided by the vertex angle defect.

The cuboctahedron and icosidodecahedron are edge-uniform and are called quasi-regular.

The snub cube and snub dodecahedron are known as "chiral", as they come in a left-handed (Latin: levomorph or laevomorph) form and right-handed (Latin: dextromorph) form. When something comes in multiple forms which are each other's three-dimensional

mirror image , these forms may be called enantiomorphs. (This nomenclature is also used for the forms of certainchemical compound s).The duals of the Archimedean solids are called the

Catalan solid s. Together with thebipyramid s and trapezohedra, these are the face-uniform solids with regular vertices.**See also***

semiregular polyhedron

*uniform polyhedron

*List of uniform polyhedra **References*** (Section 3-9)

**External links***

* [*http://demonstrations.wolfram.com/ArchimedeanSolids/ Archemedian Solids*] byEric W. Weisstein ,The Wolfram Demonstrations Project .

* [*http://www.software3d.com/Archimedean.php Paper models of Archimedean Solids and Catalan Solids*]

* [*http://www.korthalsaltes.com/archimedean_solids_pictures.html Paper models(nets) of Archimedean solids*]

* [*http://www.mathconsult.ch/showroom/unipoly/ The Uniform Polyhedra*] by Dr. R. Mäder

* [*http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra*] , "The Encyclopedia of Polyhedra" by George W. Hart

* [*http://www.cs.utk.edu/~plank/plank/origami/penultimate/intro.html Penultimate Modular Origami*] by James S. Plank

* [*http://ibiblio.org/e-notes/3Dapp/Convex.htm Interactive 3D polyhedra*] in Java

* [*http://video.google.com/videoplay?docid=7084140981126344386&q=tom+barber&hl=en Contemporary Archimedean Solid Surfaces*] Designed byTom Barber

* [*http://www.software3d.com/Stella.php Stella: Polyhedron Navigator*] : Software used to create many of the images on this page.

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