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Topic: Augmented truncated tetrahedron

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Truncated tetrahedron

	[No title]
		augmented truncated tetrahedron +------------------------------------------------------------ The augmented truncated tetrahedron is a polyhedron with 15 vertices and 14 faces.
		augmented truncated cube +------------------------------------------------------------ The augmented truncated cube is a polyhedron with 28 vertices and 22 faces.
		augmented truncated dodecahedron +------------------------------------------------------------ The augmented truncated dodecahedron is a polyhedron with 65 vertices and 42 faces.
	www.math.harvard.edu /~knill/sofia/data/polyhedra.txt (2272 words)

	Johnson solid - Cleverpedia, the ultimate encyclopedia (Site not responding. Last check: 2007-10-10)
		augmented prism 9 21 14 14 0 0 0 0 0 D3h 52 Augmented pentagonal prism
		augmented prism 11 19 10 4 4 2 0 0 0 C2v 53 Biaugmented pentagonal prism
		augmented truncated cube 32 60 30 16 10 0 0 4 0 D4h 68 Augmented truncated dodecahedron
	cleverpedia.com /Johnson_solid (1590 words)

	polyhedra.org: Quadrilateral
		5 quadrilaterals: augmented truncated cube, augmented truncated dodecahedron, pentagonal prism, square cupola, pentagonal cupola, elongated square pyramid, elongated pentagonal pyramid, elongated pentagonal dipyramid, gyroelongated square cupola, gyroelongated pentagonal cupola, pentagonal orthocupolarontunda, pentagonal gyrocupolarotunda, gyroelongated pentagonal cupolarotunda and augmented hexagonal prism
		10 quadrilaterals: biaugmented truncated cube, parabiaugmented truncated dodecahedron, metabiaugmented truncated dodecahedron, decagonal prism, elongated pentagonal rotunds, square orthobicupola, square gyrobicupola, pentagonal orthobicupola, pentagonal gyrobicupola, elongated pentagonal orthobirotunda, elongated pentagonal gyrobirotunda, gyroelongated square bicupola and gyroelongated pentagonal bicupola
		15 quadrilaterals: triaugmented truncated dodecahedron, tridiminished rhombicosidodecahedron, elongated pentagonal cupola, elongated pentagonal orthocupolarotunda and elongated pentagonal gyrocupolarotunda
	polyhedra.org /poly/polygon/4/quadrilateral (323 words)

	The Johnson Solids
		J68, the augmented truncated dodecahedron, J69, the parabiaugmented truncated dodecahedron, J70, the metabiaugmented truncated dodecahedron, and J71, the triaugmented truncated dodecahedron.
		the augmented truncated tetrahedron, and J64, the augmented tridiminished icosahedron.
		J87, the augmented sphenocorona, is formed from J86, the sphenocorona, by placing a square pyramid on one of its square faces.
	www.quadibloc.com /math/acs03.htm (2007 words)

	AP-ART Compendium - Part 2
		Tetrahedron was similar in principle to Prism except that the assembled shape was tetrahedral.
		Four of the pieces are made of truncated rhombic dodecahedron (or edge-beveled cubes) joined different ways, and the 5th piece is a single such block, for a total of 14 blocks.
		These are variations of the Augmented Four Corners (#34) made by sanding the four faces down by varying amounts to create interesting sculptural effects, especially when using contrasting woods.
	www.johnrausch.com /PuzzleWorld/apart/apartpt2.htm (8851 words)

	Kids.Net.Au - Encyclopedia > Johnson solid
		An icosahedron would be a gyroelongated pentagonal bipyramid.
		Augmented means that a pyramid has been joined to a face of the solid in question.
		Diminished means that a pyramid or cupola has been removed from the solid in question.
	www.kids.net.au /encyclopedia-wiki/jo/Johnson_solid?title=Zalgaller (475 words)

	Minimum inventory maximum diversity building system - Patent 3974600
		At this point, it is interesting to note that six of the A components 14 combine to form a tetrahedron 26, and that the B component 16 is the angular bisector to the volumetric center of the tetrahedron 26.
		The portions to be truncated are indicated in dashed outline and the solid lines remaining define a truncated tetrahedron 58, and the truncated octahedron 60.
		The truncated octahedron 60 gives rise to two space units; the truncated tetrahedron 58 gives rise to two space units; and the cuboctahedron 56 gives rise to a single space unit.
	www.freepatentsonline.com /3974600.html (14057 words)

	Top Page 1
		The largest polytope, modulo 60, is a truncated rhombic triacontahedron with 44,132 faces and 43,200 vertices (centers of an optimal packing of circles that are one degree in diameter).
		In the dual vector field, the left-handed tetrahedron, is isomorphic to the field of the right-handed tetrahedron.
		The second family is the ten polytope family of the truncated rhombic dodecahedron and the optimal spherical packing of circles for the smallest polytope in the group is the cuboctahedron.
	www.mi.sanu.ac.yu /vismath/dyke/index.html (6091 words)

	Union of Intelligent Associations: remembering the dynamic identity of a dodecameral mind
		The truncated tetrahedron is the only semi-regular solid with 12 independent axes passing through its vertices from its centre.
		Together with this 'morphic' allocation we have drawn attention to the behaviour pattern of the three major transformations from the truncated tetrahedral packing around a tetrahedral nucleus through to the equilibrium of the dymaxion or cuboctahedral configuration, and finally into the 'locked' icosahedral pattern, traversing the three major omnidirectional symmetries employed in nature.
		The "truncation" sequences in Critchlow's closest packing diagram (above) could now be viewed more dynamically as transformation processes, involving both contraction and expansion, integral to the organization of the dodecameral mind and the way in which it maintains its coherence.
	www.laetusinpraesens.org /musings/untelos.php (6890 words)

	Polyhedron, Polyhedra, Polytopes - Numericana
		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.
		Beyond F=4 (the tetrahedron of genus 0) and F=7 (the Szilassi heptahedron of genus 1) the next possibility would thus be F=12, a dodecahedron of genus 6...
	home.att.net /~numericana/answer/polyhedra.htm (5442 words)

	100.00 SYNERGY
		The cheese tetrahedron may be sliced parallel to any one, or successively all four, of its faces without losing its basic symmetry; ergo, only the tetrahedron's four-dimensional coordination can accommodate asymmetric aberrations without in any way disrupting the symmetrical integrity of the system.
		In the accommodation of asymmetric aberration the tetrahedron permits conceptual focus upon otherness, which is primitively essential to the experience of life, for it occasions life's initial awareness.
		The cosmic hierarchy is comprised of the tetrahedron's inherent, intertransformable interrelationships
	usnisa.org /synergetics/s01/p0000.html (2818 words)

	Nuts About Nets! (Site not responding. Last check: 2007-10-10)
		The 24 icosahedra lie in the cell realms of the 24 octahedra of the icositetrachoron, which is why this figure is called a “snub icositetrachoron.” The 24 blue tetrahedra also lie in the cell realms of an icositetrachoron, one positioned “dually” to the icositetrachoron of the icosahedra.
		This removes the underlying 24 dodecahedra, and since the twelve lateral cells of the dodecahedral pyramids lie in the realms of the removed dodecahedron's twelve neighbors, the 96 remaining dodecahedra become strange-looking nine-faced polyhedra: dodecahedra with tall pentagonal pyramids erected on three of their faces.
		To summarize, the cells of this figure are 10 truncated dodecahedra (in dark red), 100 pentagonal rotundae (in light green), and 200 tetrahedra (in light yellow).
	members.aol.com /Polycell/nets.html (7273 words)

	Massively Parallel Simulations of Diffusion in DensePolymeric Structures
		One may notice from Figure 1 that the distance between two adjacent tetrahedrons is equal to a carbon-carbon bond length, and the angle between three adjacent tetrahedrons is equal to a carbon-carbon-carbon angle.
		The tetrahedron or cubic cell corresponding to the shortest distance is chosen as the next position.
		The radii of all the polymer atoms are augmented by the length equal to the penetrant radius, and the unoccupied volume of the resulting model system is then calculated.
	www.cs.sandia.gov /~jfaulon/SC97/index.htm (5098 words)

	Adaptor-based sequence analysis - Patent 5888737
		In the method of claim 16, the improvement further comprising wherein after cleavage of the Type IIs endonuclease recognition site, said truncated target polynucleotide fragment is treated to remove a 5'- terminal phosphate group generated by the cleavage step.
		The method of claim 30 wherein after cleavage with the Type IIs endonuclease, the truncated target polynucleotide fragment is treated to remove a 5'-terminal phosphate group generated by the cleavage step.
		The method of claim 29 wherein the 3'- locking group is a phosphate group, and the step of converting the 3'-blocking group to a hydroxyl group is accomplished using a phosphatase.
	www.freepatentsonline.com /5888737.html (10102 words)

	[No title]
		The augmented triad differs from the major only in that the third member is raised a semi-tone.
		The major triad in color is formed by taking any one of the twelve color-centers of the ophthalmic color scale as the first member of the triad; and, reading up the scale, the fifth step (each step representing a semi-tone) determines the second member, while the third member is found in the eighth step.
		The minor triad in color is formed by lowering the second member of the major triad one step; the augmented triad by raising the third member of the major triad one step, and the diminished triad by lowering the third member of the minor triad one step.
	www.ibiblio.org /pub/docs/books/gutenberg/1/2/6/2/12625/12625-8.txt (19924 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		I* *t is base on the within density functional theory for the treatment of exchange and correlation (Hohenberg and Kohn 64, Kohn and Sham 65) and uses e.g.
		LSTART generates atomic densities which are used by DSTART to generate a starting density for a scf calculation and all the input files for the scf run: in0, in1, in2, inc and inm (according to the atomic eigenvalues).
		In addition it creates atomic potentials (which are truncated at their corresponding atomic radii and could be used to r* *un LAPW1) and optional atomic valence densities, which can be used in LAPW5 for a difference density plot.
	www.osc.edu /PET/CCM/skeleton/software/arlsoftware/wien97/guide.html (11839 words)

	Johnson solid - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-10)
		Augmented means that a pyramid or cupola has been joined to a face of the solid in question.
		When the faces altered are parallel, we add para- to the name of the operation.
		(A parabiaugmented solid has had two parallel faces augmented.) When they are not, we add meta- to the name of the operation.
	en.wikipedia.org.cob-web.org:8888 /wiki/Johnson_solid (726 words)

	XML.com: Why Choose RSS 1.0?
		This is augmented with three further vocabularies to support a simple rights language (PRL), the creation of controlled vocabularies (PCV) and inline markup (PIM).
		The interface shown here is purely for demo purposes and shows how the structured metadata terms are ready present in the feed for whatever use case may be defined.
		The primary purpose of syndicating tables of contents for serials is to provide a notification service to inform feed subscribers that a new issue has been published.
	www.xml.com /lpt/a/2003/07/23/rssone.html (1860 words)

	4.1 Elements of Fission Weapon Design
		It can be augmented by inserting one or more layers of materials of increasing density between the explosive and the dense tamper and fissile material in the center.
		Shock convergence actually steepens the Taylor wave since the front is augmented by convergence to a greater degree than the material behind the front (which is at a larger radius).
		As a rough estimate, one can conclude that the 300 kilobar pressure of Composition B could be augmented by a factor of 4 by shock reflection (doubling at the HE/Al interface, and the Al/U interface), and a factor of 5 by convergence, leading to a shock pressure of 6 megabars at the plutonium core.
	nuclearweaponarchive.org /Nwfaq/Nfaq4-1.html (21668 words)

	Mechanism of Heparin Activation of Antithrombin. ROLE OF INDIVIDUAL RESIDUES OF THE PENTASACCHARIDE ACTIVATING SEQUENCE ...
		Effect of truncating reducing-end residues of the pentasaccharide on the kinetics of pentasaccharide binding to antithrombin.
		Effect of truncating nonreducing-end residue D on the kinetics of pentasaccharide binding to antithrombin.
		DEFGH and DEFGH' and of oligosaccharides DEFG* and DEF truncated
	www.jbc.org /cgi/content/full/273/13/7478 (5978 words)

	Leymarie on Shape - the Shock Scaffold - Definitions
		Augmented Shock Scaffold: ignore the singularities of flow along sheets.
		Reduced shock scaffold: ignore the geometry of sheets and curves, but retain their existence and connectivity.
		Truncated tetrahedron (7 nodes, 19 links, 9 hyperlinks).
	www.lems.brown.edu /vision/people/leymarie/Goldsmiths/scaffold1.html (293 words)

	ElectronicStructure.org
		Saffren and J. Slater, "An augmented plane wave method for the periodic potential problem.
		Blöchl, `The Projector Augmented Wave method: Algortithm and Results', Conference of the Asian Consortium for Computational Materials Science, Bangalore, India, 2001.
		Holzwarth, A. Tackett, and G. Matthews, "A projector augmented wave (PAW) code for electronic structure calculations, part II: pwpaw for periodic solids in a plane wave basis," Comp.
	electronicstructure.org /references.asp (8743 words)

	Scientific Publications of Roald Hoffmann
		Gleiter and R. Hoffmann, Tetrahedron, 24, 5899 (1986).
		Augmented Silicon-Carbon Bond Strengths via d-_ Hyperconjugation, P.
		A Helical Face-Sharing Tetrahedron Chain with Irrational Twist, Stella Quadrangula and Related Matters, C.
	hamiltonian.chem.cornell.edu /roald_pub1.html (6817 words)

	Rob's Puzzle Page - Interlocking
		The basic plan is that of a traditional six-piece burr, but the pieces have been heavily modified and augmented to form a cube.
		Here is a beautiful version of Stewart Coffin's Augmented Four Corners puzzle, made from Canarywood and Redheart by Mark McCallum, and purchased from Cubicdissection:
		The Truncated Cube is surprisingly hefty, and very nicely finished.
	home.comcast.net /~stegmann/interlocking.htm (6008 words)

	NSDL Metadata Record -- Augmented Truncated Cube -- from MathWorld
		NSDL Metadata Record -- Augmented Truncated Cube -- from MathWorld
		The augmented truncated tetrahedron is Johnson solid J_{66} constructed by affixing a square cupola to one of the octagonal faces of a truncated cube such that the cupola's square faces are adjacent the triangular faces of the truncated cube.
		See also: Biaugmented Truncated Cube, Cupola, Johnson Solid, Truncated Cube
	nsdl.org /mr/700320 (78 words)

	[No title]
		Take the specific geometry that now seems to shape Iapetus – a truncated icosahedron, a duplicate of the “C60 fullerene.” Multiply it by the number of radii Iapetus is orbiting away from Saturn (60 …).
		And, in addition to revealing the original flened surface there, this incessant micrometorite erosion would have inevitably worn away some of the elevated vertices and edges of the original “moon” … ultimately producing the muted “truncated isocahedron” visible today ….
		Looked at in a larger context, creating a moon-sized “truncated icosahedron” would simply be the ultimate means of saying “five-sided/six-sided symmetry is crucially important in the Universe....”
	www.enterprisemission.com /moon5.htm (5152 words)

	Matches for:
		On the relation between the volume of a tetrahedron and the product of the sixteen algebraical values of its superficies
		On the centre of gravity of a truncated triangular pyramid, and on the principles of barycentric perspective
		Note on the properties of the test operators which occur in the calculus of invariants, their derivatives, analogues, and laws of combination; with an incidental application to the development in a Maclaurinian series of any power of the logarithm of an augmented variable
	www.mathaware.org /bookstore-getitem/item=CHEL-253 (4043 words)

	CMSC 437 Selected Lecture Notes
		The program split_cube.c shows a solid cube that is made up of five (5) tetrahedrons.
		This is accomplished by slightly changing the color of the vertices of the triangles that make up the faces of the tetrahedrons.
		Example programs covered: (execute and observe lighting) planets.c SphereMotion.java SphereMotion.jpg SphereMotion.html teapots.c teapots.jpg The lighting environment is the physical objects in the truncated tetrahedron plus the light(s) that may be outside this volume.
	www.cs.umbc.edu /~squire/cs437_lect.html (13707 words)

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