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Topic: List of polygons, polyhedra and polytopes

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List of lists of mathematical topics

Polygon

Star polygon

Johnson solid

Zonohedron

Disdyakis triacontahedron

Cuboctahedron

Regular polygon

Triakis tetrahedron

Deltoidal hexecontahedron

Truncated tetrahedron

Heptacontakaiheptagon

Polyhedron

Tetracontakaihexagon

Hectagon

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	Encyclopedia: List of mathematical shapes
		In geometry, an enneagon or nonagon is a nine-sided polygon.
		In geometry, the 120-cell, or hecatonicosachoron, is the convex, regular polychoron (a 4-dimensional polytope) with 120 cells (or facets).
		See also: List of mathematical topics The word esoteric generally relates to that which is known only by a restricted number of people (contrast exoteric).
	www.nationmaster.com /encyclopedia/List-of-mathematical-shapes (1537 words)

	List of lists of mathematical topics (Site not responding. Last check: 2007-10-09)
		List of harmonic analysis and representation theory topics]
		List of letters used in mathematics and science
		List of terms relating to algorithms and data structures
	www.factsite.co.uk /en/wikipedia/l/li/list_of_lists_of_mathematical_topics.html (70 words)

	Polyhedra and Polytopes (Site not responding. Last check: 2007-10-09)
		Polyhedra by Ha Quang Le - An introduction to the basic mathematics of polyhedra, illustrated with VRML and Maple code.
		Polygons, Polyhedra, Polytopes - An introduction to the subject of regular polytopes (generalizations of polygons and polyhedra) by Russell Towle.
		Polyhedra, Platonic Solids, Polytopes - Definitions, pictures, templates, and coordinates of the regular polytopes 3d and 4d.
	www.infotrend.com.tw /Science/Math/Geometry/PolyhedraandPolytopes (1064 words)

	MoneySearch.org - Unclaimed Money and Unclaimed Funds Information (Site not responding. Last check: 2007-10-09)
		Polytopes include polygons (two-dimensional), polyhedra (three-dimensional), polychora (four-dimensional), and their higher dimensional analogs.
		There are an infinite number of regular convex polygons, five regular convex polyhedra, six regular convex polychora, and three regular convex polytopes for all dimensions five or higher.
		Polygons, Polyhedra, Polytopes: Regular, rectified, and truncated polytopes with normal and hidden-detail-removed projections.
	moneysearch.org /Top/Science/Math/Geometry/Polytopes (379 words)

	Polytopes Science, Directory (Site not responding. Last check: 2007-10-09)
		Regular Polytopes Derivation of volume equations for regular polygons, polyhedra, and polytopes, with images.
		Guy's Polyhedra Pages Vertex figures, filling, faceting diagrams, stellation, defining polytopes through generators, trimethoric and trisynaptic polyhedra, space-filling polyhedra, lost stellations of the icosahedron, and links.
		Polyhedra, Platonic Solids, Polytopes Definitions, pictures, templates, and coordinates of the regular 3d and 4d polytopes.
	www.cube2.org /YzJfMjY5NDE=.aspx (212 words)

	Prism (geometry) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		Regular prisms have all equal edge lengths, and faces made of regular polygons.
		Right prisms with regular bases form one of the two infinite series of vertex-uniform polyhedra, the other series being the (additional info and facts about antiprism) antiprisms.
		The (A block in the (approximate) shape of a cube) cube is a particular type of right square prism which is also edge- and face-uniform and so counts among the (Any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent) Platonic solids.
	www.absoluteastronomy.com /encyclopedia/P/Pr/Prism_(geometry).htm (243 words)

	Zonohedron -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		A zonohedron is a (additional info and facts about convex) convex (A solid figure bounded by plane polygons or faces) polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°.
		The (A polygon with all sides and all angles equal) regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated:
		Of the (Any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent) Platonic solids, only the (A block in the (approximate) shape of a cube) cube is a zonohedron
	www.absoluteastronomy.com /encyclopedia/z/zo/zonohedron.htm (243 words)

	References
		Detailed framework for a general notion of polyhedra in which the faces are basically a path of edges, and so may be nonplanar, or the edges may go around more than once, or may be infinite, e.g., a helix.
		Rona Gurkewitz, Bennet Arnstein, Multimodular Origami: Polyhedra, Dover, 2003.
		A class of polyhedra with zones, which generalizes zonohedra, and their use in sculpture.
	www.georgehart.com /virtual-polyhedra/references.html (5153 words)

	Ortley Beach NJ
		Vertex figures, filling, faceting diagrams, stellation, defining polytopes through generators, trimethoric and trisynaptic polyhedra, space-filling polyhedra, lost stellations of the icosahedron, and links.
		Derivation of volume equations for regular polygons, polyhedra, and polytopes, with images.
		Polytopes and optimal packing of p points in n dimensional spheres.
	www.ortleybeachnj.com /index.php/Science/Math/Geometry/Polytopes (259 words)

	Polytopes: 3D View of the Web (Site not responding. Last check: 2007-10-09)
		See live article Polytope In geometry polytope means, first, the generalization to any dimension of polygon in two dimensions, and polyhedron in three dimensions One special kind of polytope is the convex hull of a finite set of points.
		Polyhedra, Platonic Solids, Polytopes - Polyhedra, Platonic Solids, Polytopes Definitions, pictures, templates, and coordinates of the regular 3d and 4d polytopes.
		Polygons, Polyhedra, Polytopes - Polygons, Polyhedra, Polytopes An introduction to the subject of regular polytopes (generalizations of polygons and polyhedra) by Russell Towle.
	www.resolve3d.com /Science/Math/Geometry/Polytopes (489 words)

	Koogle - Open Directory Project (Site not responding. Last check: 2007-10-09)
		Guy's Polyhedra Pages - Vertex figures, filling, faceting diagrams, stellation, defining polytopes through generators, trimethoric and trisynaptic polyhedra, space-filling polyhedra, lost stellations of the icosahedron, and links.
		Numericana - Polyhedra and Polytopes - Enumeration, cartesian coordinates of vertices, naming, and counting the shapes.
		Regular Polytopes - Derivation of volume equations for regular polygons, polyhedra, and polytopes, with images.
	www.koogle.net /dmoz/odp.php?browse=/Science/Math/Geometry/Polytopes (308 words)

	Polyhedra Polytopes Geometry Math Science English España
		The five regular polyhedra mapped onto the surface of their surrounding spheres, which can be rotated in java applets.
		Data on polyhedra, the different types, compounds of the shapes, stellations, stewart toroids, zonohedra, and tesselations.
		A proof that each configuration of polygons around a vertex results in a unique polyhedron, plus Java applets for rotating the images of the shapes.
	www.amigar.com /buscador/Top/10101211428-10000001 (737 words)

	Search the Internet - InternetDJ.com (Site not responding. Last check: 2007-10-09)
		Numericana - Polyhedra and Polytopes - - Enumeration, cartesian coordinates of vertices, naming, and counting the shapes.
		Polyhedra, Platonic Solids, Polytopes - - Definitions, pictures, templates, and coordinates of the regular 3d and 4d polytopes.
		Regular Polytopes - - Derivation of volume equations for regular polygons, polyhedra, and polytopes, with images.
	www.internetdj.com /search/search.php?browse=/Science/Math/Geometry/Polytopes (314 words)

	The Math Forum - Math Library - Polyhedra
		Polytope is the general term of the sequence, point, segment, polygon, polyhedron,...
		A polyhedron is the three-dimensional version of a polygon: a chunk of space with flat walls, a three-dimensional figure made by gluing polygons together.
		The study of polyhedra is one of those special areas of Mathematics which allow the amateur and expert to work with an equal delight.
	mathforum.org /library/topics/polyhedra?keyid=13695465&start_at=101&num_to_see=50 (1878 words)

	Polytopes (Site not responding. Last check: 2007-10-09)
		Additional Information: Polytopes include polygons (two-dimensional), polyhedra (three-dimensional), polychora (four-dimensional), and their higher dimensional analogs.
		An n-dimensional polytope is built up from multiple (n-1)-dimensional polytopes.
		Contains a java applet based on a model which allows for generation of multidimensional regular and semi-regular polytopes.
	www.canadiancontent.net /dir/Top/Science/Math/Geometry/Polytopes (225 words)

	Polyhedra
		There are also a few nonconvex polyhedra known that have faces and vertices all of the same type.
		The polyhedra are by default centered at the origin with a unit distance from the origin to the midpoint of the edges.
		This replaces each of the polygon faces by a pyramid with the polygon as its base.
	documents.wolfram.com /v5/Add-onsLinks/StandardPackages/Graphics/Polyhedra.html (340 words)

	The Geometry Junkyard: Polyhedra and Polytopes
		Connelly had previously discovered non-convex polyhedra which are flexible (can move through a continuous family of shapes without bending or otherwise deforming any faces); these authors prove that in any such example, the volume remains constant throughout the flexing motion.
		Stella, Windows software for visualizing regular and semi-regular polyhedra and their stellations, morphing them into each other, drawing unfolded nets for making paper models, and exporting polyhedra to various 3d design packages.
		Waterman polyhedra, formed from the convex hulls of centers of points near the origin in an alternating lattice.
	www.ics.uci.edu /~eppstein/junkyard/polytope.html (2177 words)

	The Geometry Junkyard: Many-dimensional Geometry
		Stainless steel 3d model of the 24-cell (one of the six regular polytopes in four dimensions), by Adrian Ocneanu, installed as a sculpture in the Penn State Math Department.
		He lists both general upper and lower bounds as functions of a, b, and c, and specific constructions for specific sizes of box.
		A quasi-polynomial bound for the diameter of graphs of polyhedra, G.
	www.ics.uci.edu /~eppstein/junkyard/highdim.html (1261 words)

	Science/Math/Geometry/Polyhedra and Polytopes : Science Directory
		VRML polyhedra models and raw data in the OFF format to generate them, plus images of the shapes rendered with povray.
		List of links to sites on geometric properties of polygons, polyhedra, and higher dimensional polytopes.
		Uniform polyhedra consist of regular faces and congruent vertices.
	www.123science.com /Science/Math/Geometry/Polyhedra_and_Polytopes/more2.html (351 words)

	Mathematica Documentation: Polyhedra
		The diameter of the icosahedron is reduced by a factor of 0.7 and its center is moved to the point {3, 3, 3}.
		Polyhedron converts the polygon list corresponding to the name of a polyhedron into a Graphics3D object.
		Here is the list of polygons for the tetrahedron centered at the origin.
	documents.wolfram.com /mathematica/Add-onsLinks/StandardPackages/Graphics/Polyhedra.html (377 words)

	Games Fresh : Article 'List of combinatorics topics' (Site not responding. Last check: 2007-10-09)
		A few decades ago it might have been said that combinatorics is to mathematics roughly what irritable bowel syndrome is to gastroenterology - a way to classify poorly-understood problems, and some standard remedies.
		This page is complementary to the list of graph theory topics: graph theory being the part of combinatorial mathematics that is most like a separate discipline.
		See also glossary of general topology for detailed definitions, the list of general topology topics and Main article.
	www.games-fresh.net /DisplayArticle285854.html (1163 words)

	AOL Search: Main > Science > Math > Geometry > Polyhedra and Polytopes (Site not responding. Last check: 2007-10-09)
		Three dimensional block puzzles, VRML polyhedra models, instructions for creating real-world shrinkable polyhedra models, and a gallery of images.
		An introduction to the basic mathematics of polyhedra, illustrated with VRML and Maple code.
		An introduction to polyhedra by George Olshevsky, with their properties, specifications for his custom built models, and links to other pages.
	buscador.aol.com /aol/browse?id=26941&source=subcats (818 words)

	Blue Rope Meta Search Engine (Site not responding. Last check: 2007-10-09)
		Regular, rectified, and truncated polytopes with normal and hiddendetailremoved projections.
		Contains a java applet based on a model which allows for generation of multidimensional regular and semiregular polytopes.
		Vertex figures, filling, faceting diagrams, stellation, defining polytopes through generators, trimethoric and trisynaptic polyhedra, spacefilling polyhedra, lost stellations of the icosahedron, and links.
	www.bluerope.com /cgi-bin/odp/main.cgi?/Science/Math/Geometry/Polytopes (210 words)

	Assignment P2: Fun with Polyhedra
		See also the very cool collection of links on Polyhedra and Polytopes that is part of David Eppstein's nice web collection, The Geometry Junkyard (from which I got most of the preceding links).
		A particularly elegant data structure for polyhedra is the quad-edge data structure, invented by Guibas and Stolfi.
		It can't represent all collections of polygons; it is limited to manifolds (surfaces where the neighborhood of each point is topologically equivalent to a disk; no edges shared by three faces).
	www.cs.cmu.edu /afs/andrew/scs/cs/15-463/99/pub/src/p2/p2.html (3498 words)

	Equilateral triangle - All About All (Site not responding. Last check: 2007-10-09)
		A triangle is a polygon and a 2-simplex (see polytope).
		Two triangles are said to be similar if and only if the angles of one are equal to the corresponding angles of the other.
		Lists some 1600 interesting points associated with any triangle.
	www.allaboutall.info /article/Equilateral_triangle (1988 words)

	Business Software Review : Article 'List of network theory topics' (Site not responding. Last check: 2007-10-09)
		The approach, though, is led by applications, in particular to computer networks but certainly not limited to those — for example a gene regulatory network may be modelled.
		See list of network theory topics for the scope of the area.
		Network theory is also used to describe the use of social network maps within the social sciences.
	www.business-software-review.org /DisplayArticle646625.html (128 words)

	www.miatrade.net Science Math Geometry Polytopes (Site not responding. Last check: 2007-10-09)
		» Guy's Polyhedra Pages - Vertex figures, filling, faceting diagrams, stellation, defining polytopes through generators, trimethoric and trisynaptic polyhedra, space-filling polyhedra, lost stellations of the icosahedron, and links.
		» Polyhedra, Platonic Solids, Polytopes - Definitions, pictures, templates, and coordinates of the regular 3d and 4d polytopes.
		» Regular Polytopes - Derivation of volume equations for regular polygons, polyhedra, and polytopes, with images.
	www.miatrade.net /Top/Science/Math/Geometry/Polytopes (247 words)

	AOL Search: Main > Science > Math > Geometry > Polyhedra and Polytopes (Site not responding. Last check: 2007-10-09)
		Collection of VRML polyhedra models generated by a QuickBasic program named Hedron.
		Data files and sample C code for a large number of polyhedra.
		An introduction to the subject of regular polytopes (generalizations of polygons and polyhedra) by Russell Towle.
	buscador.aol.com /aol/browse?id=26941&source=subcats (818 words)

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