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Topic: Archimedean polyhedron

	The Archimedean Honeycomb Duals
		An Archimedean polyhedron has regular but differing faces and congruent but non-regular vertices, whereas its dual has congruent but non-regular faces and regular but differing vertices, as can be seen in Figure 2.
		The family is found to have an unexpected property in that it appears to be the family of cells of the Archimedean honeycomb duals: every member of the family described is the cell of a dual, and every Archimedean honeycomb is represented.
		The only Archimedean honeycomb besides C with this property is O+T. It is said to be quasi-regular, and its dual has rhombic dodecahedral cells.
	www.steelpillow.com /polyhedra/AHD/AHD.htm (2044 words)

	Archimedean Solids
		Seven of the archimedean solids are derived from the platonic solids by the process of ‘truncation’, literally cutting off the corners of each of the platonic solids.
		The first five are the truncated tetrahedron, truncated octahedron, truncated hexahedron, truncated icosahedron and the truncated dodecahedron and these are arrived at by dividing the edges into thirds and cutting off the vertices of these points.
		A key characteristic of the archimedean solids is that each face is a regular polygon, and around every vertex, the same polygons appear in the same sequence, for example, hexagon - hexagon – triangle in the truncated tetrahedron as can be seen from the picture at the start of the section.
	www.ul.ie /~cahird/polyhedronmode/favorite.htm (482 words)

	Archimedean solid - Education - Information - Educational Resources - Encyclopedia - Music
		The Archimedean solids are known to have been discussed by Archimedes, although the complete record is lost.
		All edges of an Archimedean solid have the same length, since the faces are regular polygons, and the edges of a regular polygon have the same length.
		The duals of the Archimedean solids are called the Catalan solids.
	www.music.us /education/A/Archimedean-solid.htm (530 words)

	Johnson solid - Wikipedia, the free encyclopedia
		In geometry, a Johnson solid is a convex polyhedron, each face of which is a regular polygon, which is not a Platonic solid, Archimedean solid, prism, or antiprism.
		There is no requirement that each face must be the same polygon.
		Most of the Johnson solids can be constructed from the first few (pyramids, cupolae, and rotundae), together with the Platonic and Archimedean solids, prisms, and antiprisms.
	en.wikipedia.org /wiki/Johnson_solid (694 words)

	Archimedean Duals --- List
		Its dual; a picture of the face of the dual.
		The compound of the polyhedron and its dual.
		The middle line gives the Archimedean dual (also called a Catalan polyhedron).
	www.georgehart.com /virtual-polyhedra/archimedean-duals-index.html (41 words)

	Polyhedron Man: Science News Online, Dec. 22, 2001
		One example is the truncated icosahedron, familiar as the pattern on a soccer ball, which consists of 12 pentagons and 20 hexagons.
		During the Renaissance, he notes by way of example, Leonardo da Vinci invented a way to show the front and back of a polyhedron without confusion by depicting edges as if they were made from wooden laths and leaving the polyhedron's faces open.
		He came up with what he called the propellor [sic] operation: Start with a polyhedron, then spread apart the faces and introduce quadrilaterals so that each face is surrounded by a ring of these forms.
	www.sciencenews.org /20011222/bob13.asp (1870 words)

	Pedagoguery Software: Poly’s Polyhedra
		A polyhedron with regular polygonal faces is uniform if there are symmetry operations that take one vertex through all of the other vertices and no other points in space.
		A common heuristic for the Archimedean solids is that the arrangement of faces surrounding each vertex must be the same for all vertices.
		The next step is to ensure all of the polyhedron s faces are triangular: each non-triangular face is triangulated by connecting its vertices to a new vertex placed at the center of the face.
	www.peda.com /poly/poly.html (534 words)

	Archimedean solid - Definition, explanation
		In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices.
		They are distinct from the Platonic solids, which are composed of only one type of polygon meeting in identical vertices, and from the Johnson solids, whose regular polygonal faces do not meet in identical vertices.
		The Archimedean solids take their name from Archimedes, who discussed them in a now-lost work.
	www.calsky.com /lexikon/en/txt/a/ar/archimedean_solid.php (332 words)

	Dictionary of ConvexPoly.osax
		"polyhedron reference" returns a reference to a polyhedron.
		A "polyhedron reference" can be coerced to a polyhedron and must be released with "delete polyhedron".
		The 13 catalan polyhedra are in the same order as their archimedean duals and the result contains the name of the requested polyhedron.
	www.satimage.fr /software/en/dictionaries/dict_convex.html (700 words)

	Four Dimensional Figures Page
		Polyhedron model-making, dinosaurs, and (of course) geometric figures in the higher-dimensional Euclidean spaces.
		Below are tabulated the six Archimedean prisms and antiprisms that occur as cells of the nonprismatic convex Archimeadean polychora.
		A uniform polyhedron is one whose faces are all regular polygons and any of whose vertices (corners) may be transformed (or carried) into any of its other vertices by its symmetries.
	members.aol.com /Polycell/uniform.html (4264 words)

	Math 444 Polyhedral Links
		I found the first site useful because it listed each of the thirteen Archimedean polyhedra and gave a description of the original solid each polyhedra was made from and how to manipulate that solid to obtain an Archimedean polyhedra.
		If one were to construct a snub cube they can use the author's color coding and see that of the 32 triangular faces, the 8 red ones are the result of truncating the cube vertices and the 24 yellow ones are the result of truncating the 12 cube edges twice at different angles.
		The one I chose as a keeper archimedean polyhedra is the rhombicuboctahedron with its 24 vertices, 38 faces and 60 edges.
	www.math.washington.edu /~king/coursedir/m444a03/as/polyhedra-links.html (5045 words)

	Archimedean Solids
		A polyhedron is said to be uniform if it has regular faces and admits symmetries which will transform a given vertex into every other vertex in turn.
		All the Archimedean solids so far discussed are reflexible (by reflection in the plane that perpendicularly bisects the edge).
		In Maple, one can define an Archimedean solid by using the command Archimedean(gon,sch,o,r); where gon is the name of the polyhedron to be defined, sch the Schläfli symbol (Maple's Schläfli), o the center of the polyhedron, and r the radius of the circum-sphere.
	www.cecm.sfu.ca /~hle/polyhedra/archimedean.html (666 words)

	Stella - Create Polyhedra and Nets! Platonic, Archimedean, Catalan, Kepler-Poinsot, uniform, and dual polyhedra, their ...
		Polyhedron faces may be exploded apart by dragging the mouse with the left button down and the Shift and Ctrl keys pressed.
		By default, stellation cells are automatically chosen to recreate the original uniform polyhedron.
		Any alternative names are given for all uniform/dual polyhedra, as well as their reference and page numbers in Wenninger's Polyhedron Models and Dual Models, making this the ultimate reference for the uniform/dual polyhedra.
	home.aanet.com.au /robertw/Stella.html (1610 words)

	Tetrahedron (Site not responding. Last check: )
		A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex.
		Like all platonic solids, archimedean solids and indeed all convex polyhedra, a Tetrahedron can be folded from a single sheet of paper.
		If each edge of a Tetrahedron were to be replaced by a one ohm resistor, the resistance between any two vertices would be 1/2 ohm.
	tetrahedron.iqnaut.net (385 words)

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