- 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.

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Archimedean solid**— noun Any of a class of semi regular convex polyhedra composed of two or more types of regular polygon meeting in identical vertices … Wiktionary**archimedean solid**— noun Usage: usually capitalized A : one of 13 possible solids each of which has plane faces that are all regular polygons though not all of the polygons are of the same species and each of which has all its polyhedral angles equal … Useful english dictionary**Archimedean**— means of or pertaining to or named in honor of the Greek mathematician Archimedes. These are most commonly:* Archimedean property * Archimedean absolute value * Archimedean solid * Archimedean point * Archimedean tiling * Archimedean spiral *… … Wikipedia**Archimedean point**— An Archimedean point is a hypothetical vantage point from which an observer can objectively perceive the subject of inquiry, with a view of totality. The ideal of removing oneself from the object of study so that one can see it in relation to all … Wikipedia**Catalan solid**— In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgian mathematician, Eugène Catalan who first described them in 1865.The Catalan solids are all convex.… … Wikipedia**Johnson solid**— The elongated square gyrobicupola (J37), a Johnson solid … Wikipedia**Platonic solid**— 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 number of faces meeting at each vertex; thus, all… … Wikipedia**Near-miss Johnson solid**— In geometry, a near miss Johnson solid is a strictly convex polyhedron, where every face is a regular or nearly regular polygon, and excluding the 5 Platonic solids, the 13 Archimedean solids, the infinite set of prisms, the infinite set of… … Wikipedia**Catalan solid**— noun The dual polyhedron of an Archimedean solid Syn: Archimedean dual … Wiktionary**Johnson solid**— noun any of a class of convex polyhedra which is neither a Platonic solid, Archimedean solid, prism or antiprism … Wiktionary