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Topic: Antiprisms

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	Glossary of Terms
		Antiprism - A semi regular polyhedron constructed from two n-sided polygons and 2n triangles.
		This includes the archimedean solids, the prisms and antiprisms, and the nonconvex uniform solids.
		This includes the platonic solids, the archimedean solids, the prisms and antiprisms, and the non convex uniform solids.
	www.ul.ie /~cahird/polyhedronmode/glossary_of_terms.htm (627 words)

	Antiprism
		An antiprism is a polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles.
		Antiprisms are similar to prisms except the bases are twisted relative to each other.
		The dual polyhedra of the antiprisms are the trapezohedra[?].
	www.ebroadcast.com.au /lookup/encyclopedia/an/Antiprism.html (96 words)

	Grand antiprism at AllExperts
		In geometry, the grand antiprism or pentagonal double antiprismoid is a uniform polychoron (4-dimensional uniform polytope) bounded by 320 cells: 20 pentagonal antiprisms, and 300 tetrahedra.
		This structure is analogous to that of the 3-dimensional antiprisms.
		Conversely, the two rings of pentagonal antiprisms in the grand antiprism may be triangulated by 10 tetrahedra joined to the triangular faces of each antiprism, and a circle of 5 tetrahedra between every pair of antiprisms, joining the 10 tetrahedra of each, yielding 150 tetrahedra per ring.
	en.allexperts.com /e/g/gr/grand_antiprism.htm (395 words)

	Antiprism Information
		An n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.
		Antiprisms are similar to prisms except the bases are twisted relative to each other: the vertices are symmetrically staggered.
		If n=3 then we only have triangles; we get the octahedron, a particular type of right triangular antiprism which is also edge- and face-uniform, and so counts among the Platonic solids.
	www.bookrags.com /wiki/Antiprism (497 words)

	antiprism
		An antiprism is like a prism in that it contains two copies of any chosen regular polygon, but is unlike a prism in that one of the copies is given a slight twist relative to the other.
		Antiprisms are named square antiprisms, pentagonal antiprisms, and so on.
		The simplest, the triangular antiprism, is better known as the octahedron.
	www.daviddarling.info /encyclopedia/A/antiprism.html (179 words)

	NSDL Metadata Record -- Antiprism -- from MathWorld
		The nets are particularly simple, consisting of two n-gons on top and bottom, separated by a ribbon of 2n triangles, with the two n-gons being offset by one ribbon segment.
		The duals of the antiprisms are the trapezohedra.
		The graph corresponding to the skeleton of an antiprism is known, not surprisingly, as an antiprism graph.
	nsdl.org /mr/698926 (122 words)

	Augmenting the Great Cubicuboctahedron
		The octagrammic faces are excavated with octagrammic antiprisms, the square faces excavated with square pyramids, and the triangular faces with triangular antiprisms or octahedra.
		)/3, and (3,3,3,3) from the octagrammic antiprisms, the square pyramids and octahedra respectively.
		The triangles of the octagrammic antiprisms are shown in purple, the triangles of the square pyramids are blue and the octahedra are yellow.
	web.ukonline.co.uk /polyhedra/uniform/augmented/19.html (327 words)

	Learn more about Polyhedron in the online encyclopedia. (Site not responding. Last check: )
		Any polyhedron which is vertex-uniform can be deformed slightly to form a vertex-uniform polyhedron with regular polygons as faces.
		Convex forms include two infinite series, one of prismss and one of antiprisms, as well as the thirteen Archimedean solids.
		There are an infinite number of non-convex forms, but surprisingly only a finite number of convex shapes other than the prisms and antiprisms.
	www.onlineencyclopedia.org /p/po/polyhedron.html (605 words)

	[No title]
		It can also be thought of as a star antiprism - one of a family of polyhedra in which two star polygons (here the degenerate 4/2; the pentagram is another example) are joined by triangles that join edges on one side to vertices on the other.
		The Grand Antiprism is closely related to the 600-cell, in roughly the same way that the pentagonal antiprism is related to the icosahedron.
		Similarly, the two rings of antiprisms can be filled with non-regular tetrahedra - ten tetrahedra going in from the center of each antiprism to its center, and a lens-shaped ring of five joining the centers of each two adjacent antiprisms in the chain to each of their shared edges.
	cs.stmarys.ca /~dawson/images3.html (1580 words)

	Prisms and Antiprisms
		An antiprism also consists of two copies of any chosen regular polygon, but one is given a slight twist relative to the other, and they are connected with a band of alternately up and down pointing triangles.
		And, a special case of the antiprism is the octahedron (when the chosen top and bottom face is a triangle).
		Kepler was the first to discuss antiprisms, and recognize the connection between prisms and the Archimedean solids.
	www.georgehart.com /virtual-polyhedra/prisms-info.html (289 words)

	Ivars Peterson's MathTrek - Euler Bricks and Perfect Polyhedra
		You can readily extend the same approach to other polyhedra, such as prisms and antiprisms.
		An antiprism consists of two identical polygons in parallel planes joined in such a way that all the other faces are isosceles triangles.
		Peterson and Jordan go on to investigate interesting links between integer octahedra and integer antiprisms.
	www.maa.org /mathland/mathtrek_10_25_99.html (596 words)

	Archimedean solid
		The prisms and antiprisms, though they meet the above criteria, are typically excluded from the Archimedean solids because they do not have a higher polyhedral symmetry.
		These solids were known to be discussed by Archimedes, although the complete record is lost.
		This search culminated in the work of Johannes Kepler circa 1619, who defined prisms, antiprisms, and the non-convex solids known as Kepler solids.
	www.ebroadcast.com.au /lookup/encyclopedia/ar/Archimedean_solid.html (498 words)

	The Johnson Solids
		While the infinite families of prisms and antiprisms (with squares and equilateral triangles making up the round belt between the two regular polygons of arbitrary type) are excluded from the set of Johnson solids, these shapes can still be added to other shapes to make new Johnson solids.
		These are J84, the snub disphenoid, J85, the snub square antiprism, J86, the sphenocorona, J87, the augmented sphenocorona, J88, the sphenomegacorona, J89, the hebesphenomegacorona, J90, the disphenocingulum, and J92, the triangular hebesphenorotunda.
		J85, the snub square antiprism, is a highly symmetrical shape.
	www.quadibloc.com /math/acs03.htm (2007 words)

	Uniform Tessellations and Polyhedra (Site not responding. Last check: )
		They are familiar to most people interested in geometry: the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron.
		A prism has two n-gonal faces; one of these faces may be obtained from the other by translation in the direction perpendicular to the plane of the face.
		An antiprism also has two n-gonal faces; one may be obtained from the other by translation as before, followed by a rotation through π/n radians.
	www.monmouth.com /~chenrich/UniformTessellations.html (2796 words)

	trprf (Site not responding. Last check: )
		Finally, excavate (augment in the opposite direction) the resulting tower with two 8/3 antiprisms, then two 8/5-antiprisms, until you are back where you started.
		This polyhedron is topologically equivalent to a torus (a doughnut shape with one hole).
		You need to use an n-gonal antiprism, where n is even and less than 3.
	www.geocities.com /stonemason89/trprf.html (202 words)

	Klein's Quartic Curve
		This embedding is made as follows: take 4 triangular prisms, each with 2 triangular faces and 3 square faces, and place them at the vertices of a large tetrahedron.
		Then take 6 square antiprisms: solids with 2 square faces, and 8 triangular faces which join every vertex of each square face to an edge of the opposite one.
		Bend and twist the antiprisms and glue their square faces to those of the triangular prisms.
	gregegan.customer.netspace.net.au /SCIENCE/KleinQuartic/KleinQuartic.html (1265 words)

	The regular prisms and antiprisms
		There are two infinite classes of facially regular polyhedra: The prisms and antiprisms.
		In figure 15 we show the regular prism and antiprism with a hexagonal face.
		Find the axes of symmetry and the planes of symmetry of a (a) regular prism, and a (b) regular antiprism.
	nothung.math.uh.edu /~mike/hti/handouts/handout4/node9.html (171 words)

	Electronic Resources - 3D Geometry in the 3rd Grade: Sorting and Describing Polyhedra
		For the seventeen students that focused on shapes, nine had some subset of the pyramids, nine had some subset of the dipyramids, eight had a subset of the antiprisms, and three had a subset that combined prisms and antiprisms.
		One student, Rob, included C (pentagonal antiprism) and A (hexagonal prism) in his group because they “are the same.” The student noticed that both of these objects are similar in appearance, vaguely resembling a drum.
		The fact that he included the pentagonal antiprism rather than the hexagonal antiprism is indicative that he did not pay attention to the specific feature of the number of edges in the base and top of the polyhedra he chose.
	my.nctm.org /eresources/view_article.asp?article_id=7076&page=3 (804 words)

	Multidimensional Glossary (Site not responding. Last check: )
		An altered pentagonal prism is a pentagrammatic antiprism.
		If we allow higher-dimensional antiprisms to have antiprisms as well as simplexes among their lateral facets joining two base polytopes, then three such uniform antiprisms are known in four-space and two more in five-space.
		The dual of an antiprism in three-space is an antibipyramid, and the dual of a polytopal prism is a bipyramid based on the dual of the base of the prism.
	members.aol.com /Polycell/glossary.html (16070 words)

	Prism Maker
		This program generates prisms and antiprisms and crossed antiprisms and/or their duals, based on any desired polygon.
		antiprism based on the 15/7 polygon in the window above.
		If you are a programmer, you may like to look at the VRML source code which this page generates to describe an object.
	www.georgehart.com /virtual-polyhedra/prism-maker-subpanel.html (124 words)

	4-dimensional Antiprisms.
		In this page 4-dimensional antiprisms are defined the way to preserve analogy with the 3-dimensional case (see a page of 'Literka' 3-dimensional antiprisms for some description and pictures) as much as it is possible, without falling into trivialities.
		Because bases of 4-dimensional antiprism are regular polyhedrons and between them there is a semi-regular polyhedron - cross section by a parallel hyperplane, 4-dimensional antiprisms can be used (by taking appropriate cross sections) for polyhedrons morphing.
		Take a regular tetrahedron as a base of antiprism P. Polyhedron S dual to R is also a regular tetrahedron.
	www.literka.addr.com /polytopes/antiprisms.htm (772 words)

	Arbelos: Polyhedra posters
		Excluding the prisms and antiprisms, there are 75 uniform polyhedra, 18 of them convex and 57 non-convex.
		Apart from prisms and antiprisms, the convex uniform polyhedra are the five Platonic solids and the thirteen Archimedean (or semi-regular) solids.
		Sixteen are illustrated on The Beauty of Mathematics poster Truncation; the other two are the tetrahedron, and the truncated tetrahedron shown alongside.
	www.arbelos.co.uk /Polyhedra.html (458 words)

	Tom Gettys - Nonconvex Prisms & Antiprisms
		This article describes the Nonconvex Prisms and Antiprisms, which share the same relationship to the nonconvex Uniform Polyhedra as the convex Prisms and Antiprisms have to the Archimedian solids.
		The Nonconvex Antiprisms are formed in exactly the same way as their convex counterparts; the only difference is that the top and bottom are nonconvex regular polygons.
		A Crossed Antiprism is simply a nonconvex antiprism in which the faces pass through the center of the polyhedron.
	home.comcast.net /~tpgettys/nonconvexprisms.html (302 words)

	Examples of Integrated, Multi-set Concept Schemes: Polygons and polyhedra
		4.1 There are only four facially regular prisms and antiprisms using the faces of the Platonic polyhedra (see 3.2): triangular prism, pentagonal prism, square antiprism, pentagonal antiprism (excluding the Platonic polyhedra: cube, tetrahedron, octahedron) (Pugh, 21) There four duals are: triangular dipyramid, pentagonal dipyramid, trapezoidal octahedron, trapezoidal deca- hedron.
		7.1 There are7 facially regular prisms and antiprisms using the 3 polygonal faces of the Platonic polyhedre (see 3.2): triangular prism, square prism/cube, pentagonal prism, tetrahedron, triangular antiprism/octahedron, square antiprism, pentagonal antiprism (i.e.
		10.3 There arel0 facially regular prisms and antiprisms using the 6 polygonal faces of the Platonic and Archimedean polyhedra (although excluding the latter): triangular prism, pentagonal prism, hexagonal prism, octagonal prism, decagonal prism, square antiprism, pentagonal antiprism, hexagonal prism, octagonal antiprism, decagonal entiprism (Pugh 27)
	www.laetusinpraesens.org /docs80s/84nsetsx/x18.php (1214 words)

	Polyhedron at AllExperts
		in 1954 and later confirmed by J. Skilling, there are exactly 75 uniform polyhedra, plus an infinite number of prisms and antiprisms.
		The convex ones consist of the prisms and antiprisms and the Archimedean solids.Non-convex semi-regular are listed below.
		* Trapezohedron (such as the cube), are dual to an antiprisms.
	en.allexperts.com /e/p/po/polyhedron.htm (1964 words)

	Amazon.com: "hexagonal antiprisms": Key Phrase page (Site not responding. Last check: )
		The centers of the icosahedra occupy the origin of a cubic...
		and the In 12 hexagonal antiprisms are additionally centred by single Na atoms.
		The network is made of 12-bonded icosahedra (closo-In,,) and 6-bonded hexagonal antiprisms (arachno-In,,) in ratio 1:3.
	www.amazon.com /phrase/hexagonal-antiprisms (517 words)

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