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Topic: Augmented pentagonal prism

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Biaugmented pentagonal prism

Tetrahedron

	[No title]
		augmented triangular prism +------------------------------------------------------------ The augmented triangular prism is a polyhedron with 7 vertices and 8 faces.
		augmented pentagonal prism +------------------------------------------------------------ The augmented pentagonal prism is a polyhedron with 11 vertices and 10 faces.
		augmented hexagonal prism +------------------------------------------------------------ The augmented hexagonal prism is a polyhedron with 13 vertices and 11 faces.
	www.math.harvard.edu /~knill/sofia/data/polyhedra.txt (2272 words)

	Augmented pentagonal prism - Wikipedia, the free encyclopedia
		In geometry, the augmented pentagonal prism is one of the Johnson solids (J
		As the name suggests, it can be constructed by augmenting a pentagonal prism by attaching a square pyramid (J
		The 92 Johnson solids were named and described by Norman Johnson in 1966.
	en.wikipedia.org /wiki/Augmented_pentagonal_prism (89 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.
		Elongated means that a prism has been joined to the base of the solid in question or between the bases of the solids in question.
		Augmented means that a pyramid or cupola has been joined to a face of the solid in question.
	en.wikipedia.org /wiki/Johnson_solid (684 words)

	Johnson solid
		An octahedron would be a square bipyramid, a cuboctahedron would be a triangular gyrobicupola, and an icosidodecahedron would be a pentagonal gyrobirotunda.
		An icosahedron would be a gyroelongated pentagonal bipyramid.
		Augmented means that a pyramid has been joined to a face of the solid in question.
	www.ebroadcast.com.au /lookup/encyclopedia/jo/Johnson_solid.html (450 words)

	Method and apparatus for dodecahedral imaging system - Patent 5023725
		The pentagon, the basis of the twelve-sided dodecahedron, encompasses the most of all, 75.71% of the optimal circle, and only six pentagons are required to cover half of a sphere.
		Projecting all three pentagons in an overlapping arrangement also depends on a projection module that also has this wide field of view, and is aligned as well to the vertex, meaning that it would have to have the same pyramidical structure as the camera.
		The altitude of a pentagonal section from the middle of an edge to the center is 0.807017, shown at 226, and one-half of a dodecahedral edge is 0.587785, shown at 227.
	www.freepatentsonline.com /5023725.html (15269 words)

	Polyhedron, Polyhedra, Polytopes, ... - Numericana
		In such families, the polyhedron is named using the adjective corresponding to the name of the polygon it's built on (e.g., "hexagonal").
		For example, if you cut a prism with a plane containing some edge of either base polygon (but not intersecting the other), this "half" prism is called a wedge (it includes the base polygon and its featured edge).
		Elongated: By replacing (one of) the largest m-sided polygon, with an m-gonal prism (that polygon may not be a face of the polyhedron, but an "internal" polygon with apparent edges).
	home.att.net /~numericana/answer/polyhedra.htm (5061 words)

	acrohedra
		We shall temporarily introduce a third limitation; that is for the time being we shall only consider polygons that occur in the uniform polyhedra or in the Johnson Solids.
		This reduces the polygons under consideration to the triangle, square, pentagon, hexagon, octagon and decagon.
		I have heard these polygons referred to (with tongue in cheek) as the 'polydronic' polygons after the Polydron polyhedral construction kits.
	web.ukonline.co.uk /polyhedra/acrohedra/acrohedra.html (860 words)

	Unusual Coordination
		Molybdenite has 6-fold coordination in which the molybdenum atoms are surrounded by six sulfur atoms at the vertices of a triangular prism.
		The coordination polyhedron is a square pyramid on one face of a triangular prism, sometimes called an augmented triangular prism.
		Another way to picture this solid is to begin with a pentagonal dipyramid, cut two adjacent equatorial edges, squeeze from the sides to open the cut, and insert two equilateral triangle faces in the gap.
	www.uwgb.edu /dutchs/PETROLGY/coordinationx.htm (726 words)

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		O groups at distances from 2.73 to 2.97 Å, with a mean distance of 2.89 Å; this is a very restricted range of distances for such a large coordination polyhedron, and hence there is not the usual problem of determining whether the longest distances represent significant bonds.
		Selenium is coordinated to three oxygen atoms arranged in a triangle with the central cation significantly displaced from the plane of the oxygen atoms (Fig.
		In the real structure (upper layer), the Ba coordination is a tri-augmented monocapped triangular prism, whereas in the idealized Pmnm structure (lower layer) the Ba coordination is a gable disphenoid (Johnson 1966).
	www.umanitoba.ca /science/geological_sciences/labs/xray/publish/guilleminite.htm (1036 words)

	Section 6 (Site not responding. Last check: 2007-10-13)
		Pentagonal pyramid: base a slightly irregular pentagon, 4 edge lengths all 1, 5th edge length sqrt(2); all 5 lateral edges length sqrt(2), making one lateral triangle equilateral, the other 4 isosceles
		Faces: 90 squares (60 joining pentagonal prisms to hexagonal prisms, 30 joining hexagonal prisms to hexagonal prisms), 24 pentagons (all joining truncated icosahedra to pentagonal prisms), 40 hexagons (all joining truncated icosahedra to hexagonal prisms)
		Pentagonal pyramid: base a slightly irregular pentagon, 4 edge lengths all 1, 5th edge length tau; all 5 lateral edges length sqrt(2)
	members.aol.com /Polycell/section6.html (3336 words)

	Nuts About Nets!
		Indeed, two pentagonal faces of the dodecahedron are removed, six others are extended in their planes into two trapezoids and four kite-shaped quadrilaterals (“phylloids”), and the other four faces remain unchanged.
		The pentagons are fuchsia, the outer trapezoids are beige and their inner counterparts are red, and the phylloids are turquoise.
		In the snub cuboctahedral prism, one base will be left-handed and the other will be right-handed, because when the mantle prisms fold up in four-space, the net on one side of the mantle folds up and the net on the other side folds down.
	members.aol.com /Polycell/nets.html (7273 words)

	Stella: Polyhedron Navigator
		Note that all pentagons in this model are of the same type (they each have the same relationship to the model as a whole), so only one facet need be created.
		Other models are augmented with a cupola instead, such as J66, the augmented truncated cube, which is a truncated cube with a square cupola (J4) attached to one side.
		The user also has the option to augment using a pyramid or cupola (which require a regular face to be selected) or a prism, or augmenting from memory.
	web.aanet.com.au /robertw/PolyNav/PolyNavigator.html (12506 words)

	Johnson Polyhedra
		For example, a biaugmented triangular prism is denoted Y4P3Y4 (a square pyramid built onto two adjacent faces of a triangular prism).
		Thus, a triaugmented triangular prism is denoted (Y4)3P3 (a square pyramid built onto all three faces of a triangular prism).
		A diminished icosahedron is a gyroelongated pentagonal pyramid
	www.uwgb.edu /dutchs/symmetry/johnsonp.htm (480 words)

	names & notations (Site not responding. Last check: 2007-10-13)
		Each face of the "expanded" polyhedron is rotated by the same angle and in the same direction, thus this leads to two enantiomorph polyhedra (mirror images) depending on the rotation's direction.
		The n-kis operator introduces a new vertex on the axis of each n-face, and therefore n triangles (in fact each x-face is augmented with a x-pyramid); so the tetrakis-cube has 6x4=24 triangular faces, thus is an icositetrahedron.
		A compound polyhedron is the union of several identical or related polyhedra arranged to preserve a polyhedral symmetry: the anticube is a compound of two regular tetrahedra, my favourite is the compound of five regular tetrahedra.
	www.ac-noumea.nc /maths/amc/polyhedr/names_.htm (1238 words)

	Decomposable Polyhedra
		I will also have a few of prism symmetry, but these are not nearly as interesting.
		Primarily this will consist of prisms sliding together to form larger prisms, or augmentations being added to a central figure in prism symmetry fashion.
		The third category are the ones that interest me most, and the components connect together with a symmetry greater than that of a prism.
	galileo.spaceports.com /~adoskey/polyhedra/DecomposablePolyhedra.html (516 words)

	Pedagoguery Software: Poly’s Polyhedra
		Although all of the Archimedean solids have this property, so does the elongated square gyrobicupola (Johnson solid which is not an Archimedean solid.
		After the Platonic and Archimedean solids, the only remaining convex uniform polyhedra with regular faces are prisms and anti-prisms.
		Dipyramids are duals of prisms; deltohedra are duals of anti-prisms.
	www.peda.com /poly/poly.html (534 words)

	prism - 247 info (Site not responding. Last check: 2007-10-13)
		dove optics augmented hexagonal prism optics support for 2 & of a apollo risc veon kites from HQ, Eolo difference between and pyramid as lenses, and mirrors.
		Sælger Premium hundefoder geometry abbe is triangular used for prism geometry prism in geometry and quartz types from own wacky products including PRISM, Prism ImmuBank, FTP cube rectangular plastic, rubber, sufaces.
		This levelling staff, prism system, prism pole, prisms Swarovski crystal suncatchers with a pentagonal Reactor and harness and Stockists of Flexifoil, Spirit optics geometry and prism prism equation square rectangular apollo-domain triangular is triangular used second newton white dove camera lucida rectangular right prism experiments
	247-info.dyndns.org /content/prism (174 words)

	Johnson's polyhedra (Site not responding. Last check: 2007-10-13)
		Johnson's polyhedra are the convex polyhedra with regular faces - thus all edges have same length - (as the regular, the archimedean, the prisms and anti-prisms) but with vertices of different types: there are 92.
		You get most of them by modifying pyramids, archimedean solids, prisms or anti-prisms.
		Only five are chiral (exist in two mirror image versions) : the gyroelongated polyhedra (modified by inserting an antiprism in the place of a facet) J44 to J48.
	www.ac-noumea.nc /maths/amc/polyhedr/p_Johnson_.htm (154 words)

	augmented pentagonal prism - OneLook Dictionary Search (Site not responding. Last check: 2007-10-13)
		We found 2 dictionaries with English definitions that include the word augmented pentagonal prism:
		Tip: Click on the first link on a line below to go directly to a page where "augmented pentagonal prism" is defined.
		Augmented Pentagonal Prism : Eric Weisstein's World of Mathematics [home, info]
	www.onelook.com /?w=augmented+pentagonal+prism (85 words)

	prism - ffind (Site not responding. Last check: 2007-10-13)
		rectangular geometry rectangular right dove products including PRISM, Prism ImmuBank, FTP support for 2 & second newton white difference between and pyramid triangular optics plastic, rubber, sufaces.
		the rectangular right angle right prism in geometry of a geometry dove optics camera lucida State University's mapping program.
		prism dispersion Reactor and harness and prism veon square and quartz types from levelling staff, prism system, prism pole, prisms produces a of color own wacky apollo risc rectangular a pentagonal apollo-domain of a the friendly Editor.
	ffind.ath.cx /content/prism (110 words)

	Session D40 - Poster Session I.
		The lowest energy isomer for Cu_7 and Ag_7 is a pentagonal bipyramid structure with a C_5v symmetry, while the C_3v trigonal structure emerges as the higher energy isomer.
		In the case of Na_7 and K_7 the energy difference between the two isomers obtained in theoretical calculations is small enough that for all practical purposes the two isomers could be considered degenerate.
		The calculated hyperfine properties of the pentagonal bipyramid clusters are in excellent agreement with those measured and are used to conclusively identify the structure of these clusters.
	flux.aps.org /meetings/YR01/MAR01/abs/S1560.html (18752 words)

	iqexpand.com (Site not responding. Last check: 2007-10-13)
		There is a near-Johnson solid which can be constructed by inscribing regular nonagons inside the eight triangular faces of a regular octahedron, then joining the free edges to the 24 triangles and...
		Examples include the augmented triangular prism (Johnson solid J_(49)), boat, gyrobifastigium (Johnson solid J_(26)), heptagonal pyramid, hexagonal prism, (regular) octahedron, square dipyramid...
		Johnson Solid-state Advanced Oil Metering (SAM) system Description: The Solid-state Advanced Oil Metering System (SAM) controls fuel oil delivery in relation to the combustion air by utilizing a...
	johnson_solid.iqexpand.com (779 words)

	The Project Gutenberg eBook of Treatise on Light, by Christiaan Huygens
		This was, that this crystal, as well as that from Iceland, has a double refraction, though less evident.
		For having had cut from it some well polished Prisms of different sections, I remarked in all, in viewing through them the flame of a candle or the lead of window panes, that everything appeared double, though with images not very distant from one another.
		Whence I understood the reason why this substance, though so transparent, is useless for Telescopes, when they have ever so little length.
	www.gutenberg.org /dirs/1/4/7/2/14725/14725-h/14725-h.htm (12243 words)

	Dimensionality, Spring 2005 (Site not responding. Last check: 2007-10-13)
		Jessica asked about ways to generalize a pentagon into n dimensions.
		As you may know, in three dimensions there are five regular polyhedra, namely, the tetrahedron (3-sx), cube (3-cube), octahedron (3-cross-polytope, with f-vector (1, 6, 12, 8, 1)), dodecahedron (f-vector (1, 20, 30, 12, 1) and has pentagonal 2-faces), and icosahedron (f-vector (1, 12, 30, 20, 1) with triangular 2-faces).
		We could consider a dodecahedron to be a generalization of a pentagon.
	www.cs.xu.edu /~smbelcas/dims.html (5851 words)

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		Why the incident and refracted Rays produce one another reciprocally.
		Why Reflexion within a triangular glass prism is suddenly augmented when the Light can no longer penetrate.
		That bodies which cause greater Refraction also cause stronger Reflexion.
	www.ibiblio.org /pub/docs/books/gutenberg/1/4/7/2/14725/14725.txt (13646 words)

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