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Topic: Triakis tetrahedron

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Truncated tetrahedron

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		tetrahedron +------------------------------------------------------------ The tetrahedron is a polyhedron with 4 vertices and 4 faces.
		triakis tetrahedron +------------------------------------------------------------ The triakis tetrahedron is a polyhedron with 8 vertices and 12 faces.
		triakis icosahedron +------------------------------------------------------------ The triakis icosahedron is a polyhedron with 32 vertices and 60 faces.
	www.math.harvard.edu /~knill/sofia/data/polyhedra.txt (2272 words)

	Poliedri (Site not responding. Last check: 2007-10-08)
		The triakis tetrahedron is the dual of the truncated tetrahedron.
		The trigonal pyramids are all regular tetrahedrons, whose bases correspond to the midpoints of the edges of the octahedron.
		The dual of the triakis icosahedron is the truncated dodecahedron but neither the centroids of the former nor the centroids of the latter are capable of generating their duals.
	g.casagrande.home.att.net /poliedri/poliedri_text.html (4932 words)

	Oriental Planet - tetrahedron kite
		tiling 3^6 in the Euclidean plane and the tetrahedron 3^3, cube 4^3, and icosahedron 3^5 on the...
		A tetrahedron is a large kite-shaped indicator sometimes located beside the runway and may move freely or be set manually.
		TETRAHEDRON ASYMMETRY (1997) 8 (11) 1721 1724 276268...
	www.bigorientalplanet.com /kite/tetrahedronkite (791 words)

	Truncated tetrahedron - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-08)
		Canonical coordinates for the vertices of a truncated tetrahedron centered at the origin are (±3, ±1, ±1), (±1, ±3, ±1), (±1, ±1, ±3), where the ± has the same parity for each coordinate, that is, all coordinates have an even number of minuses (or all have an odd number).
		It has 4 regular hexagonal faces, 4 regular triangular faces, 12 vertices and 18 edges.
		A famous depiction of an irregular truncated tetrahedron is in Albrecht Dürer's engraving, "Melencolia I".
	en.wikipedia.org /wiki/Truncated_tetrahedron (105 words)

	CRYSTALLOGRAPHY - LoveToKnow Article on CRYSTALLOGRAPHY (Site not responding. Last check: 2007-10-08)
		Six kinds of primitive forms were distinguished, namely, the cube, the regular octahedron, the regular tetrahedron, a rhombohedron, an octahedron with a rhombic base, and a double six-sided pyramid.
		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.
		Six of the simple forms, the cube, tetrahedron, rhombic dodecahedron, deltoid dodecahedron, triakis-tetrahedron and pentagonal dodecahedron, are geometrically the same in thi class as in either the tetrahedral or pyritohedral classes.
	www.1911encyclopedia.org /C/CR/CRYSTALLOGRAPHY.htm (20186 words)

	Octahedron (Site not responding. Last check: 2007-10-08)
		Thus the volume is four times that of a regular tetrahedron with the same edge length, while the surface area is twice (because we have 8 vs. 4 triangles).
		The interior of the compound of two dual tetrahedra is an octahedron, and this compound, called the stella octangula, is its first and only stellation.
		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.
	www.tocatch.info /en/Octahedron.htm (359 words)

	Clearing up the market cycle... best Truncated Tetrahedron (Site not responding. Last check: 2007-10-08)
		The truncated tetrahedron is one of the thirteen Archimedean solids.
		Augmented Truncated Tetrahedron -- from MathWorld Augmented Truncated Tetrahedron -- from MathWorld The augmented truncated tetrahedron is Johnson solid J_{65} constructed by affixing a triangular cupola to one of the hexagonal faces of a...
		The Inradius, Midradius, and Circumradius for a truncated tetrahedron with are...
	ascot.pl /th/Fourier5/Truncated-Tetrahedron.htm (495 words)

	Of a tetrahedron - Logos Tetrahedron Concert Hall
		In quantum chaos a tetrahedron is considered as a three dimensional billiard in a A free point particle is confined within the tetrahedron and is
		Tetrahedron Beamer - A major factor in our well being is the free flow of energy throughout our bodies.
		Concerts in the Tetrahedron:, next concert, current concerts, concert archive The Logos Tetrahedron concerthall is at Bomastraat 26-28, in Ghent.
	www.newinfoindex.com /?q=of-a-tetrahedron (535 words)

	Triakis (Site not responding. Last check: 2007-10-08)
		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)

	Polyhedron, Polyhedra, Polytopes, ... - Numericana
		The dihedral angle between a pair of faces is supplementary to that angle; its cosine is 1/3 and its value is about 70.52878° (this may be called a cubic angle, for a reason which follows).
		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.
		Based on this 2-D case [and, to a lesser extent, on the 3-D case] it would seem that such an inner ball [disk, sphere, or n-dimensional hypersphere] would always be small enough to fit inside the simplex [equilateral triangle, regular tetrahedron, n-dimensional regular simplex] formed by the centers of the congruent balls.
	home.att.net /~numericana/answer/polyhedra.htm (4643 words)

	TETRAHEDRAL - Online Information article about TETRAHEDRAL
		The hemihedral form lhkklof the icositetrahedron; it is bounded by twelve isosceles triangles arranged in threes over the tetrahedron faces.
		The hemihedral form {hkll of the hexakis-octahedron; it is bounded by twenty-four scalene triangles and is the general form of the class.
		combination of Tetrahedron, Cube and Rhombic Tetrahedron and Rhombic Dodecahedron.
	encyclopedia.jrank.org /TAV_THE/TETRAHEDRAL.html (803 words)

	Truncated tetrahedron -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		The truncated tetrahedron is an (Click link for more info and facts about Archimedean solid) Archimedean solid.
		It has 4 regular (A six-sided polygon) hexagonal faces, 4 regular (Click link for more info and facts about triangular) triangular faces, 12 vertices and 18 edges.
		A famous depiction of an irregular truncated tetrahedron is in (Click link for more info and facts about Albrecht Dürer) Albrecht Dürer's engraving, "Melencolia I".
	www.absoluteastronomy.com /encyclopedia/T/Tr/Truncated_tetrahedron.htm (133 words)

	Dodecahedra (Site not responding. Last check: 2007-10-08)
		Another is the triakis tetrahedron, but it would also be odd to call it any kind of dodecahedron and obscure the fact that it is an Archimedean dual.
		It has tetrahedral symmetry with six mirror planes, and can be derived from the tetrahedron by dividing the triangles into thirds and then puffing it out a bit.
		There are many possibilities here, but some very interesting ones are the tetrahedral stellations of the dodecahedron and the little-known, yet quite beautiful, stellations of the triakis tetrahedron.
	euch3i.chem.emory.edu /proposal/www.li.net/~george/virtual-polyhedra/dodecahedra.html (978 words)

	Multidimensional Glossary (Site not responding. Last check: 2007-10-08)
		For example, a regular tetrahedron may be obtained as a partial faceting of a cube.
		Thus, for example, the vertex figure of the demicube is a rectified triangle, which is a smaller triangle, the vertex figure of a tetrahedron (the demicube).
		The vertex figure of the demitesseract is a rectified tetrahedron, which is an octahedron, the vertex figure of a regular hexadecachoron (the demitesseract).
	members.aol.com /Polycell/glossary.html (16079 words)

	The International Bone Rollers' Guild (Site not responding. Last check: 2007-10-08)
		Joseph Fjelstad patented a die in 1994 (left) that functions as a four sided die, but is actually a Truncated Tetrahedron.
		The Dual to the Truncated Tetrahedron is called the Triakis Tetrahedron.
		Like its geometric cousin, the Regular Tetrahedron, the Triakis Tetrahedron is a little bit tricky to number for use as a die.
	members.aol.com /dicetalk/polyh3.htm (590 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)

	Wooden Polyhedra Models (Site not responding. Last check: 2007-10-08)
		These are the five dodecahedra in which every face is identical and every dihedral angle is equal.
		In the front are the rhombic dodecahedron and the triakis tetrahedron.
		Start with a cube for practice, and avoid tricky ones like the tetrahedron, which have very sharp dihedral angles.
	www.georgehart.com /virtual-polyhedra/wooden-models.html (240 words)

	Download Poly (32-bit) v1.05 Shareware software - Softlookup Downloads
		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=16054 (286 words)

	Final Stellation of Triakis Tetrahedron (Site not responding. Last check: 2007-10-08)
		Home > Gallery > My Models > Stellated Polyhedra > Final Stellation of Triakis Tetrahedron.
		This model is the final stellation of the triakistetrahedron.
		I suggest you don't knock your polyhedra to the floor and then stand on them, they tend to get dents in them like this one.
	home.aanet.com.au /robertw/StelTriakisTet.html (99 words)

	Triakis tetrahedron -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Triakis tetrahedron -- Facts, Info, and Encyclopedia article
		(Click link for more info and facts about truncated tetrahedron) truncated tetrahedron
		A triakis tetrahedron is a (Click link for more info and facts about catalan solid) catalan solid which looks a bit like an overinflated (Any polyhedron having four plane faces) tetrahedron.
	www.absoluteastronomy.com /encyclopedia/T/Tr/Triakis_tetrahedron.htm (98 words)

	Bruce L. Chilton (Site not responding. Last check: 2007-10-08)
		This he abandoned once he realized there were literally millions of them.
		He also embarked on stellating a simpler Archimedean dual, the triakis tetrahedron.
		This solid has 12 congruent isosceles triangular faces (making it a “triangular dodecahedron”), and its set of stellations turned out to be pretty manageable—just a few hundred.
	members.aol.com /Polycell/chilton.html (2144 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-08)
		Truncated tetrahedron Click on picture for large version.Click [here]; for spinning version.
		Type Archimedean Faces 4 triangles4 hexagons Edges 18 Vertices 12 Vertex configuration 3,6,6 Symmetry group tetrahedral (Td) Dual polyhedron triakis tetrahedron Properties convex, semi-re..
		In mathematics, truncation is the term used for reducing the number of digits right of the decimal point, by discarding the least significant ones.
	www.hostingciamca.com /browse.php?title=T/TR/TRU (10953 words)

	Computer Graphics - Available Polyhedrons (Site not responding. Last check: 2007-10-08)
		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/ig/week1/pol.htm (508 words)

	incredibly silly question: D12? [Archive] - RPGnet Forums
		cuboctohedron, IIRC), and the triakis tetrahedron, dual of the truncated tetrahedron.
		But I can't recall where; never seen triakis tetrahedra with numbers on them.
		Oh; the 4-space equivalent of the icosahedron has 600 tetrahedral sides.
	forum.rpg.net /archive/index.php/t-71313.html (2151 words)

	Draft Comprehensive Conservation Plan December 1998
		These include the following buildings: 7 bunkers, 2 guard/watch towers, 3 concrete buildings, and 1 quonset hut.
		Other structures or facilities within the proposed Refuge boundaries include: runway lighting, helicopter wash pad, electrical vaults (concrete holes 2 to 10 feet deep), storm sewers, blast fence ruins, fences, power poles, wheels up landing aid, and a tetrahedron structure.
		The land portion of the Refuge is composed entirely of engineered fill that was placed over submerged land or tidal flats within San Francisco Bay between 1939 and 1940 (Nichols and Wright 1971).
	www.fws.gov /pacific/planning/alameda_ccp.htm (17069 words)

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