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Topic: Polyhedra

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	Polyhedra - the memory-resident SQL DBMS for embedded applications (Site not responding. Last check: 2007-11-06)
		Polyhedra is built on the concept of expressing all the various data sources in a uniform manner by using a common relational data model.
		This is a Polyhedra client component that uses the same scripting language, CL, that is used inside the database for specifying the 'methods' that are to be attached to tables and triggered when changes occur.
		Polyhedra supports a wide range of code connectivity options including several for C++ that enable interfaces to be constructed for external applications and devices.
	www.polyhedra.com /overview.htm (1867 words)

	Table of Infinite Regular Polyhedra
		Polyhedra are surfaces composed of polygons such that each edge is adjacent to two polygons (or "faces").
		Regular polyhedra are those that are composed of only one type of regular polygon (regular polygons have all edge lengths and angles equal).
		Polyhedra that close on themselves have a finite number of faces, but it's possible to describe polyhedra constructions that are infinite.
	www.superliminal.com /geometry/infinite/infinite.htm (1134 words)

	Polyhedron, Polyhedra, Polytopes, ... - Numericana
		Polyhedra in certain families are named after one of their prominent polygons.
		Polyhedra and Polytopes (Zonohedra = Hypercube Shadows) by Russell Towle.
		The most "generic" way is to use for polyhedra the same naming scheme as for polygons, by counting the number or their faces: Thus, a tetrahedron has 4 faces, a pentahedron has 5, a dotriacontahedron (also called triacontakaidihedron) has 32 faces.
	home.att.net /~numericana/answer/polyhedra.htm (4643 words)

	Counting Polyhedra - Numericana
		If both chiralities of the tetragonal antiwedge were counted as distinct, there would be 3 polyhedra with 6 faces and 6 vertices (instead of 2, including the pentagonal pyramid), and there would be 8 hexahedra (instead of 7).
		The number of polyhedra with n nodes and n faces is also known beyond what is shown in the table.
		Steven Dutch gives a detailed enumeration of polyhedra with 4,5,6,7 faces, as well as all 257 octahedra (8 faces and 6, 7, 8, 9, 10, 11 or 12 vertices) and many of the 2606 enneahedra (9 faces) too.
	home.att.net /~numericana/data/polyhedra.htm (997 words)

	The Polyhedra Embedded Database, in memory database, realtime database,sql database, vx works database, linux database, ...
		Polyhedra is a lightweight, high performance in memory database.
		Polyhedra brings together the benefits of SQL database technology with a powerful set of high performance features designed specifically for the embedded market.
		Polyhedra goes well beyond the limits of traditional database management systems, empowering the system designer with performance and features not available elsewhere.
	www.polyhedra.com (409 words)

	Polyhedra (Site not responding. Last check: 2007-11-06)
		The cube and the tetrahedron are examples of Regular Polyhedra, also called Platonic Solids.
		A polyhedron is called regular if the faces are congruent (same size and shape) regular polygons and the same number of faces meet at each vertex.
		Tom Gettys' Polyhedra site has computer generated images of platonic solids, archimedean solids, and more.
	mathforum.org /sum95/math_and/poly/polyhedra.html (271 words)

	The Geometry Junkyard: Polyhedra and Polytopes (Site not responding. Last check: 2007-11-06)
		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.
		HypArr, software for modeling and visualizing convex polyhedra and plane arrangements, now seems to be incorporated as a module in a larger Matlab library for multi-parametric analysis.
		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)

	polyhedra (Site not responding. Last check: 2007-11-06)
		Johannes Kepler, in 1619, found two polyhedra which are simultaneously regular and not convex - the small stellated dodecahedron and the big stellated dodecahedron.
		The previous table points to a certain distribution of the 5 regular polyhedra in 3 classes: Tetrahedron (dual of itself), Cube and Octahedron, Dodecahedron and Icosahedron.
		In the model formed by a tetrahedron and its dual (which is also a tetrahedron) presented in the duality table, if we enlarge the interior tetrahedron so that the edges of both tetrahedron are at the same distance of the common center, we obtain a composed polyhedron - the stella octangula.
	www.atractor.pt /mat/Polied/poliedros-e.htm (309 words)

	Regular polyhedra
		Another term for the regular (convex) polyhedra is Platonic bodies.
		a 4-dimensional polyhedron has sides that are themselves 3-dimensional polyhedra, etc. Let S, F, E, V be 3-dimensional sides, faces (2d), edges and vertices of a 4-dimensional polyhedron.
		The number of holes in a polyhedra is called its genus.
	www.cut-the-knot.org /do_you_know/polyhedra.shtml (1138 words)

	The Regular Polyhedra
		All polyhedra have dual figures, although these figures may not be polyhedra in the traditional sense: The dual figures of some polyhedra may have vertices, edges, and even faces at infinity, while the dual figures of other polyhedra may have coincident vertices, edges, or faces.
		Experienced model-makers will find building the regular polyhedra to be “old hat”; this atlas is intended more to hook novice model-makers into acquiring an interest in these figures, so that they may later go on to build more elaborate figures of their own design.
		Because the two polyhedra have the same midradius (the distance from the center to the midpoint of any edge), each edge of the octahedron perpendicularly bisects a corresponding edge of the cube, and vice versa.
	members.aol.com /Polycell/regs.html (11220 words)

	Straw Polyhedra (Site not responding. Last check: 2007-11-06)
		Straw polyhedra are skeletal polyhedra whose edges are non-bendable (8 inches long or less) colored straws, held together by thin cotton twine threaded through the straws.
		Straw polyhedra are very light and attractive looking, and they are a very valuable teaching help in the early and middle grades.
		Be sure that congruent polyhedra are not hung in the same position, with one string attached to one vertex.
	www.math.nmsu.edu /breakingaway/Lessons/straw/straw.html (1462 words)

	Amazon.com: Books: Polyhedra (Site not responding. Last check: 2007-11-06)
		Recently, polyhedra and their symmetries have been cast in a new light by combinatorics and group theory.
		The author strikes a balance between covering the historical development of the theory surrounding polyhedra and rigorous treatment of the mathematics involved.
		transitive polyhedra, rhombic polyhedra, flexible polyhedra, flexible octahedron, flexible polyhedron, star polyhedron, whole polyhedron, stellation process, compound polyhedra, elementary polyhedra, stellation patterns, colouring type, prismatic symmetry, regular star polyhedra, indirect symmetries, solid angle containing, stellated forms, uniform polyhedra, five octahedra, ten tetrahedra, vertex transitive, form the solid angle, great icosahedron, proper colourings, polyhedral network
	www.amazon.com /exec/obidos/tg/detail/-/0521664055?v=glance (1062 words)

	Waterman Polyhedra
		This slider allows you to explore the first 2000 polyhedra of the infinite series (there is a different series for each origin choice).
		Traditionally, Waterman Polyhedra are generated with the large sphere centered on one of the atoms.
		The polyhedra in this series have the symmetry of a flat rectangle whose top and bottom faces are the same (so turning it over is a symmetry).
	dogfeathers.com /java/ccppoly.html (2229 words)

	Read This: Polyhedra
		Polyhedra are among the most beautiful objects in mathematics.
		Polyhedra, on the other hand, cannot always be dissected and reassembled to form another shape.
		Several different definitions have been used, and they give rise to several different families of polyhedra, each with a claim to being regular.
	www.maa.org /reviews/polyhedra.html (592 words)

	Virtual Reality Polyhedra
		Polyhedra have an enormous aesthetic appeal and the subject is fun and easy to learn on one's own.
		You may choose to simply view the virtual objects for their timeless, serene aesthetics, or to read the related mathematical background material at various levels of depth.
		I believe the best way to learn about polyhedra is to make your own paper models or other models.
	www.georgehart.com /virtual-polyhedra/vp.html (597 words)

	Robert W. Gray's Polyhedra Encyclopedia
		I present the polyhedra as they occur in the "120 Polyhedron Matrix".
		The data is also given for the occurrence of the polyhedra in the 5 Octahedron matrix, which I call the "alternate 120 Polyhedron."
		All of the subdivisions and combinations of polyhedra used in Fuller's Synergetics books are included.
	www.rwgrayprojects.com /rbfnotes/polyhed/pindex.html (182 words)

	Roy and Geometric Solids
		The puzzles are based on polygons and polyhedra, and both require precision in their making.
		Not shown are the cube, octahedron and icosahedron, having, respectively, 6, 8 and 20 faces.
		For those of you who would like to know more about polyhedra, I have made a list of books that have helped me understand more about these beautiful objects.
	www.geocities.com /~rrice2/roy_bio/roy.html (620 words)

	Pavilion of Polyhedreality
		To learn more than you ever wanted to know about polyhedra, you will want to visit my Encyclopedia of Polyhedra.
		It is intended as a museum of objects, a reference work, and a tutorial of sorts, all dedicated to the serene, timeless beauty of polyhedra and their interrelationships.
		Over 1000 polyhedra are on display here --- from the familiar to the never-before-seen --- far more than have ever been assembled or collected anywhere.
	www.georgehart.com /pavilion.html (698 words)

	Uniform Polyhedra (Site not responding. Last check: 2007-11-06)
		Allowing for non-convex faces and vertex figures, there are 75 such polyhedra, as well as 2 infinite families of prisms and antiprisms.
		A recently discovered uniform way of computing their vertex coordinates [Harel93] is the basis for a program to display all of these solids, among which are many beautiful and stunning shapes.
		The animations use a rather high number of frames for smoother motion and are, therefore, quite large.
	www.mathconsult.ch /showroom/unipoly (425 words)

	52B: Polytopes and polyhedra
		Here are a few files concerning geometric objects made from straight pieces: polygons, polyhedra, and generalizations.
		Schreiber, Peter: "What is the true number of semiregular (Archimedean) solids?", Festschrift on the occasion of the 65th birthday of Otto Krötenheerdt.
		Unusual four-dimensional polyhedra: the 24-cell, 120-cell, and 600-cell.
	www.math.niu.edu /~rusin/known-math/index/52BXX.html (982 words)

	Archimedean Polyhedra (Site not responding. Last check: 2007-11-06)
		The Archimedean polyhedra are polyhedra with regular polygon faces.
		Except for the truncated tetrahedron, lower right, all the Archimedean polyhedra are modifications of the cube-octahedron pair or the dodecahedron-icosahedron pair.
		In each case in the last row the threefold axis face is colored differently from the extra or snub faces.
	www.uwgb.edu /dutchs/symmetry/archpol.htm (336 words)

	Math Links- Teachers Network
		Crystals - Students studying polyhedra enjoy seeing the structures as they occur in the real world.
		Polyhedra in the Classroom This unit by Suzanne Alejandre introduces the concepts of surface area and volume while focusing on the importance of measurement.
		Students calculate the surface area of a rectangular prism; name the characteristics (number of edges, faces, vertices, and the shape of the face) of 6 specific polyhedra (cube, tetrahedron, octahedron, dodecahedron, icosahedron, and cuboctahedron); demonstrate their understanding of the characteristics of polyhedra; and explore polyhedra in the real world through crystalline structures and 'buckyballs'.
	www.teachersnetwork.org /dcs/math/links/mlpolyhedra.htm (201 words)

	Making the Polyhedra (Site not responding. Last check: 2007-11-06)
		These are notes on some of the polyhedra that you can make with the basic modules (triangle, square, pentagon, hexagon).
		I have made most of these polyhedra, and some colorings to look much better than others (at least to me).
		In general, I've found that it's best to make sure that all three edges of any triangle are not the same color.
	www.cs.utk.edu /~plank/plank/pics/origami/penultimate/polyhedra.html (179 words)

	The Geometry Junkyard: Unfolded Polyhedra (Site not responding. Last check: 2007-11-06)
		A common way of making models of polyhedra is to unfold the faces into a planar pattern, cut the pattern out of paper, and fold it back up.
		Unfolding some classes of orthogonal polyhedra, Biedl, Demaine, Demaine, Lubiw, Overmars, O'Rourke, Robbins, and Whitesides, CCCG 1998.
		It turns out that the familiar cross hexomino pattern for folding cubes can also be used to fold three other polyhedra with four, five, and eight sides.
	www.ics.uci.edu /~eppstein/junkyard/unfold.html (717 words)

	Polyhedra
		The Archimedean, or semi-regular polyhedra, are 'facially' regular.
		The symbol used to describe the regular polyhedra is a combination of integers and exponents.
		The base indecates the number of sides of the regular polygonal face: 3.4.5 would mean the a triangle, a square and a pentagon were in volved.
	www.faculty.fairfield.edu /jmac/rs/polyhedra.htm (492 words)

	The Platonic Solids (Site not responding. Last check: 2007-11-06)
		Our aim now is to show that for any pair of number n and m the values of the other parameters, f, e, and v are determined uniquely.
		But as an exercise you may wish to modify the dismantling procedure to remove all doubts in your mind.
		A similar dismantling procedure could be designed for a tessellation of a polyhedron by polyhedra, but in that case it is not always possible.
	www.math.utah.edu /~alfeld/math/polyhedra/polyhedra.html (952 words)

	Tom Gettys - Polyhedra Hyperpages (Site not responding. Last check: 2007-11-06)
		The study of polyhedra is one of those special areas of Mathematics that allows the amateur and expert to work with an equal delight.
		To begin our investigation into Polyhedra, then, we will adopt a set of highly restrictive attributes and see if we can discover what solids have these properties in common.
		The set of polyhedra that satisfy these constraints is known as the Platonic Solids.
	home.comcast.net /~tpgettys/poly.html (510 words)

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