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	Octahedron - Wikipedia, the free encyclopedia
		A regular octahedron is a Platonic solid composed of eight faces each of which is an equilateral triangle four of which meet at each vertex.
		The regular octahedron is a special kind of triangular antiprism and of square bipyramid, and is dual to the cube.
		The vertices of the octahedron lie at the midpoints of the edges of the tetrahedron, and in this sense it relates to the tetrahedron in the same way that the cuboctahedron and icosidodecahedron relate to the other Platonic solids.
	en.wikipedia.org /wiki/Octahedron (376 words)

	[No title]
		octahedron +------------------------------------------------------------ The octahedron is a polyhedron with 6 vertices and 8 faces.
		triakis tetrahedron +------------------------------------------------------------ The triakis tetrahedron is a polyhedron with 8 vertices and 12 faces.
		triakis octahedron +------------------------------------------------------------ The triakis octahedron is a polyhedron with 14 vertices and 24 faces.
	www.math.harvard.edu /~knill/sofia/data/polyhedra.txt (2272 words)

	Poliedri (Site not responding. Last check: 2007-10-18)
		Hence, the hexahedron is the dual of the octahedron.
		The triakis tetrahedron is the dual of the truncated tetrahedron.
		The dual of the tetrakis hexahedron is the truncated octahedron from the tetrakis hexahedron.
	g.casagrande.home.att.net /poliedri/poliedri_text.html (4932 words)

	CRYSTALLOGRAPHY - LoveToKnow Article on CRYSTALLOGRAPHY (Site not responding. Last check: 2007-10-18)
		A regular octahedron and a cube are thus each symmetrical with respect to the following elements of symmetry: a centre of symmetry, thirteen axes of symmetry (of three kinds), and nine planes of symmetry (of two kinds).
		An octahedron thus consists of eight similar faces, and a cube is bounded by six faces all of which have the same surface characters, and parallel to each of which all the properties of the crystal are identical.
		85 and 86; the former is elongated in the direction of one of the edges of the octahedron, and the latter is flattened parallel to one pair of faces.
	www.1911encyclopedia.org /C/CR/CRYSTALLOGRAPHY.htm (20186 words)

	Octahedron -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-18)
		An octahedron (plural: octahedra) is a (A solid figure bounded by plane polygons or faces) polyhedron with eight faces.
		A regular octahedron is a (Any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent) Platonic solid composed of eight faces each of which is an equilateral triangle four of which meet at each vertex.
		The regular octahedron is a special kind of triangular (Click link for more info and facts about antiprism) antiprism and of square (Click link for more info and facts about bipyramid) bipyramid, and is dual to the (A block in the (approximate) shape of a cube) cube.
	www.absoluteastronomy.com /encyclopedia/o/oc/octahedron.htm (413 words)

	Read about Octahedron at WorldVillage Encyclopedia. Research Octahedron and learn about Octahedron here! (Site not responding. Last check: 2007-10-18)
		The regular octahedron is a special kind of triangular antiprism and of square
		tetrahedra is an octahedron, and this compound, called the stella octangula, is its first and only stellation.
		One can also divide the edges of an octahedron in the ratio of the golden mean to define the vertices of an
	encyclopedia.worldvillage.com /s/b/Octahedral (288 words)

	TETRAHEDRAL - Online Information article about TETRAHEDRAL
		There are only three dyad axes of symmetry, which coincide with the crystallographic axes; in addition there are three triad axes and a centre of symmetry.
		Here the cube, octahedron, rhombic dodecahedron, triakis-octahedron and icositetrahedron are geometrically the same as in the first class.
		36-39) of these forms with the cube and the octahedron are common in pyrites.
	encyclopedia.jrank.org /TAV_THE/TETRAHEDRAL.html (803 words)

	Encyclopedia: Octahedron
		In solid geometry and some ancient physical theories, a Platonic solid is a convex polyhedron with all its faces being regular polygons of the same size and shape, and the same number of faces meeting at each of its vertices.
		The Elongated square gyrobicupola, a Johnson solid 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.
		The ohm is the SI derived unit of electrical resistance (derived from the ampere and the watt).
	www.nationmaster.com /encyclopedia/Octahedron (1061 words)

	"Occult Chemistry - Chapter XIV
		Each Carbon atom is an octahedron in outline; each is composed of eight funnels, four positive and four negative.
		Each octahedron in the figure is a Carbon atom of eight funnels; the difference in the electrical quality of the funnels is shown by light faces of the octahedron for positive, and dark faces for negative funnels.
		The arrangement of the octahedrons in Graphite is such that, in each ring of six, a positive funnel is linked to a negative, and vice versa.
	www.tphta.ws /TPH_OC14.HTM (2058 words)

	Stars (M. C. Escher) - Open Encyclopedia (Site not responding. Last check: 2007-10-18)
		One of the lesser stars in the lower right corner of this print is a solid octahedron 3-compound.
		Two stella octangula appear, one solid compound in the lower left and one beveled wireframe in the upper right.
		A small triakis octahedron appears in the middle right.
	www.open-encyclopedia.com /Stars_%28M._C._Escher%29 (193 words)

	Australia diamond deposits, geology, exploration, mining, use - Part I
		All were small, the largest being the octahedron of 5 5/8 carats mentioned above, which, when cut, formed a beautiful colourless brilliant, weighing 3 5/16 carats.
		The stones average in weight about 1/4 carat, and vary considerably in colour, passing from perfectly water-clear through various shades of yellow, pale green, and brown to almost fl; a twinned octahedron of a beautiful dark-green colour was once found.
		The commonest crystalline forms are the octahedron, which occurs both as simple and twinned crystals, the rhombic dodecahedron, triakis-octahedron, and hexakis-octahedron; one crystal with the form of a deltoid dodecahedron has been found.
	www.kanada.net /alluvial/diamondGeology43.html (1193 words)

	Multidimensional Glossary (Site not responding. Last check: 2007-10-18)
		This compound is the colonel of the 24/1/2 regiment.
		The vertex figure of this compound is the regular octahedron whose corners are at the centers of the faces of the cube that is the vertex figure of the icositetrachoron.
		The octahedron vertex figure has just one uniform faceting, into a tetrahemihexahedron (the demicross polyhedron), which is the vertex figure of the demicross polychoron that has the same vertices, edges, and faces as the hexadecachoron.
	members.aol.com /Polycell/glossary.html (16079 words)

	P214: Computer Graphics 1 - Coursework Groups
		Small Triakis Octahedron (24 triangles; dual of the Truncated Cube; a cumulation of the Octahedron)
		Triakis Icosahedron (60 triangles; dual of the Truncated Icosahedron)
		Triakis Tetrahedron (12 triangles; dual of the Truncated Tetrahedron; a cumulation of the Tetrahedron)
	www.soi.city.ac.uk /~dcd/ig2/groups.htm (297 words)

	Triakis (Site not responding. Last check: 2007-10-18)
		I am a grade 8 teacher and have come across the term "Triakis" used with Tetrahedron, octahedron, and hexahedron.
		names of solids derived respectively from the icosahedron, octahedron, and tetrahedron by erecting a triangular pyramid on each face, thus multiplying the original number of faces by three.
		Something interesting that I found when seraching for the word triakis is that the Leopard Shark is Triakis semifasciata The name makes me wonder if its teeth are in the shape of triangular pyramids.
	mathcentral.uregina.ca /qq/database/QQ.09.00/grant1.html (246 words)

	Zonish Polyhedra
		As a consequence they are also equivalent to expansions of the seed polyhedron (or their dual rhombic polyhedra) by Mrs.
		The faces of the seed snub dodecahedron are not all separated by the six zones.
		triakis octahedron + 12 zones --- the star here is based on the face normals, not the axes of symmetry of the seed triakis octahedron, but again has octahedral symmetry.
	www.georgehart.com /virtual-polyhedra/zonish_polyhedra.html (1353 words)

	Octahedron Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-18)
		Looking For octahedron - Find octahedron and more at Lycos Search.
		Find octahedron - Your relevant result is a click away!
		Look for octahedron - Find octahedron at one of the best sites the Internet has to offer!
	www.alienartifacts.com /encyclopedia/Octahedron (515 words)

	convex polyhedra 4
		Among the the Platonic and Archimedean solids the cuboctahedron is the only polyhedron inscribed in a sphere with radius equal to its edge (as the hexagon is the only regular polygon inscribed in a circle with radius egal to its side).
		We notice the poverty of the tetrahedron family: the tetrahedron truncated using the midpoints of the edges is the octahedron, the snub tetrahedron is the icosahedron, but the truncation using the thirds of the edges gives the truncated tetrahedron.
		Generalization to the non convex polyhedra: f + v = e + 2 - t where t is the number of tunnels of the polyhedron (its genus).
	www.ac-noumea.nc /maths/amc/polyhedr/convex4_.htm (572 words)

	The International Bone Rollers' Guild
		The Dual to the Truncated Cube is called the Triakis Octahedron.
		The Dual to the Truncated Dodecahedron is the Triakis Icosahedron.
		It consists of twenty of the same sort of pyramids we've seen before, this time arranged in a pattern reminiscent of the Icosahedron.
	members.aol.com /dicetalk/polyh4.htm (196 words)

	Encyclopedia: Triakis octahedron
		Spinning triakis octahedron, made by me using POV-Ray, see image:poly.
		In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other.
		The truncated octahedron, also known as a Mecon, is an Archimedean solid.
	www.nationmaster.com /encyclopedia/Triakis-octahedron (178 words)

	Polyhedron, Polyhedra, Polytopes, ... - Numericana
		From the center of a regular octahedron, two vertices are seen separated either by a right angle (90°) or by a flat angle (180°).
		This adds up to 8, instead of 9, because the regular octahedron happens to be counted twice (as a Platonic solid and a square dipyramid)...
		The other three are the truncated octahedron (at left), the great rhombicosidodecahedron (at right) and the great rhombicuboctahedron.
	home.att.net /~numericana/answer/polyhedra.htm (4643 words)

	Stella: Polyhedron Navigator
		If we had started with the cube's dual, the octahedron, a similar thing would have happened, past the truncated octahedron until we again reached the cuboctahedron.
		This last part is played in reverse to get from the cuboctahedron to the octahedron, thus completing the transition from cube to octahedron.
		Take two consecutive edges in one of the square faces and connect their midpoints to the centre of the face, and to the intermediate vertex to form a quadrilateral.
	home.aanet.com.au /robertw/PolyNav/PolyNavigator.html (12506 words)

	The Polyhedra of M.C. Escher
		Stars, wood engraving, 1948, illustrated below, features the compound of three octahedra, a compound of two cubes, and the stella octangula, all in both outline and solid form, along with dozens of other polyhedra.
		Flatworms, lithograph, 1959, incorporates the space-filling properties of the tetrahedron and octahedron.
		Waterfall, lithograph, 1961, illustrated above, features the compound of three cubes and the first stellation of the rhombic dodecahedron.
	www.georgehart.com /virtual-polyhedra/escher.html (436 words)

	The ConvexPoly osax (Site not responding. Last check: 2007-10-18)
		1 Cube, 2 Octahedron, 3 Tetrahedron, 4 Icosahedron, 5 Dodecahedron.
		1 Rhombic Dodecahedron, 2 Disdyakis Triacontahedron, 3 Disdyakis Dodecahedron, 4 Rhombic Triacontahedron, 5 Deltoidal Hexecontahedron, 6 Deltoidal Icositetrahedron, 7 Pentagonal Icositetrahedron, 8 Pentagonal Hexecontahedron, 9 Triakis Octahedron, 10 Triakis Icosahedron, 11 Pentakis Dodecahedron, 12 Tetrakis Hexahedron, 13 Triakis Tetrahedron.
		The optional parameter scale defaults to 100 and may be used to get coordinates suitable for drawing in a window or for any other purpose.
	www.satimage.fr /software/en/convex_osax.html (1019 words)

	Download Poly (16-bit) v1.05 Shareware software - Softlookup Downloads (Site not responding. Last check: 2007-10-18)
		You can design Platonic solids (tetrahedrons, cubes, octahedrons, dodecahedrons, and icosahedrons), Archimedean solids (truncated tetrahedrons, cuboctahedrons, truncated cubes, and more), and prisms and anti-prisms (triangular prisms, pentagonal prisms, hexagonal prisms, and more).
		In addition, Poly can generate Johnson solids (square pyramid, pentagonal pyramid, triangular cupola, and more), Catalan solids (Triakis tetrahedron, rhombic dodecahedron, Triakis octahedron, and more), and dipyramids and deltohedrons (triangular dipyramid, pentagonal dipyramid, hexagonal dipyramid, and more).
		Maple V is a powerful mathematical problem-solving and visualization system used world-wide in education, research, and industry.
	www.softlookup.com /display.asp?id=16053 (287 words)

	Occult Chemistry - Chapter 14
		" There is still one more peculiarity, which however is not represented in the model The whole molecule is, as I have said, a flattened octahedron, and of course its eight sides are triangles.
		But in the middle of each of these eight sides-or rather aver the middle of it-hovers a single floating Carbon atom, floating out at right angles to the face of the triangle, pointing straight away from its centre.
		Tiny as this Carbon atom is, it produces a curious effect We know how each chemical atom makes a shape for itself by pushing back surrounding matter-a shape which is really illusory, like the octahedron for the Carbon atom, whose sides are actually the mouths of funnels.
	www.subtleenergies.com /ormus/oc/chaptr14.htm (2394 words)

	Properties of Dice
		(E) N=8, M=3, R=4, V=6 (octahedron, standard d8)
		The top three illustrations are done by me, the rest are done by Ed Pegg, Jr.
		The regular octahedron (d8) and the cube (d6) are special cases of the infinite series having M=3 and M=4, respectively.
	www.fantasylibrary.com /lounge/diceprop.htm (3085 words)

	References
		How to cut a cube into 15 pieces and reassemble as a rhombic dodecahedron, or into 17 pieces and reassemble as a truncated octahedron.
		Anthony Smith, "Stellations of the Triakis Tetrahedron," Mathematical Gazette, Vol.
		Describes and illustrates stellations of the triakis tetrahedron.
	www.georgehart.com /virtual-polyhedra/references.html (5153 words)

	Computer Graphics - Available Polyhedrons
		Other Polyhedra of comparable difficulty may be chosen.
		Note that Platonic Solids (Tetrahedron, Hexahedron (Cube), Octahedron, Dodecahedron and Icosahedron), the Cuboctahedron and the Stella Octangula are not available, as they are either too simple or there are too many examples of coding them already available (or both).
		To request allocation of a polyhedron not explicitly listed above, include a paper definition of the polyhedron on paper, with sufficient drawing(s) to make it readily recognisable.
	www.soi.city.ac.uk /~dcd/ig2/week01/pol.htm (508 words)

	Polyhedra - Fleurent G.M. - Homage to Ugo Adriano Graziotti
		Some are quite large, so it can take some time.
		The origin of the Triakis Tetrahedron, the Triakis Octahedron and the
		The origin of the Tetrakis Hexahedron, the Hexakis Octahedron
	users.skynet.be /polyhedra.fleurent/Graziotti/UAGraziotti.htm (311 words)

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