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Topic: Pentagonal dipyramid

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Gyroelongated square dipyramid

triangular dipyramid

Pentagonal dipyramid

elongated pentagonal dipyramid

elongated triangular dipyramid

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	[No title]
		pentagonal prism +------------------------------------------------------------ The pentagonal prism is a polyhedron with 10 vertices and 7 faces.
		pentagonal dipyramid +------------------------------------------------------------ The pentagonal dipyramid is a polyhedron with 7 vertices and 10 faces.
		elongated pentagonal dipyramid +------------------------------------------------------------ The elongated pentagonal dipyramid is a polyhedron with 12 vertices and 15 faces.
	www.math.harvard.edu /~knill/sofia/data/polyhedra.txt (2272 words)

	Kids.Net.Au - Encyclopedia > Johnson solid (Site not responding. Last check: 2007-10-20)
		An octahedron would be a square bipyramid, a cuboctahedron would be a triangular gyrobicupola, and an icosidodecahedron would be a pentagonal gyrobirotunda.
		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.
		An icosahedron would be a gyroelongated pentagonal bipyramid.
	www.kids.net.au /encyclopedia-wiki/jo/Johnson_solid?title=Norman_Johnson (475 words)

	SAPO - Pesquisa por triangular dipyramid
		Triangular Dipyramid; Pentagonal Dipyramid; Hexagonal Dipyramid; Octagonal Dipyramid;
		dipyramid, and J14, the elongated triangular dipyramid; J8, the elongated...
		The triangular (or trigonal) dipyramid is one of the 8 convex deltahedra,...
	pesquisa.sapo.pt /?...&q=triangular+dipyramid&t=4&fs=10&limit=20 (314 words)

	The Johnson Solids (Site not responding. Last check: 2007-10-20)
		J13, the pentagonal dipyramid, J28, the square orthobicupola, J29, the square gyrobicupola, J31, the pentagonal gyrobicupola, J30, the pentagonal orthobicupola, J32, the pentagonal orthocupolarotunda, and J33, the pentagonal gyrocupolarotunda.
		The two component pieces of the pentagonal dipyramid both came from the icosahedron, the two component pieces of the square orthobicupola and the square gyrobicupola both came from the small rhombicuboctahedron, and the two component pieces of the pentagonal orthobicupola and the pentagonal gyrobicupola both came from the small rhombicosidodecahedron.
		J24, the gyroelongated pentagonal cupola and J25, the gyroelongated pentagonal rotunda.
	www.quadibloc.com /math/acs03.htm (2007 words)

	Bipyramid - Wikipedia, the free encyclopedia
		An n-agonal bipyramid or dipyramid is a polyhedron formed by joining an n-agonal pyramid and its mirror image base-to-base.
		The referenced n-agon in the name of the bipyramids is not an external face but an internal one, existing on the primary symmetry plane which connects the two pyramid halves.
		Three bipyramids can be made out of all equilateral triangles, the octahedron (tetragonal bipyramid), which counts among the Platonic solids, and the triangular and pentagonal bipyramids, which count among the Johnson solids.
	en.wikipedia.org /wiki/Bipyramid (364 words)

	polyhedra.org: Triangle (Site not responding. Last check: 2007-10-20)
		8 triangles: metabiaugmented hexagonal prism, augmented truncated tetrahedron, bilunabirotunda, octahedron, square antiprism, elongated square dipyramid, triangular orthobicupola, square orthobicupola, square gyrobicupola, elongated triangular orthobicupola, elongated triangular gyrobicupola, elongated square gyrobicupola, biaugmented pentagonal prism and parabiaugmented hexagonal prism
		10 triangles: parabiaugmented dodecahedron, metabiaugmented dodecahedron, metabidiminished icosahedron, parabidiminished rhombicosidodecahedron, metabidiminished rhombicosidodecahedron, gyrate bidiminished rhombicosidodecahedron, pentagonal antiprism, pentagonal rotunda, pentagonal dipyramid, elongated pentagonal dipyramid, elongated pentagonal rotunds, pentagonal orthobicupola, pentagonal gyrobicupola, elongated pentagonal orthobicupola, elongated pentagonal gyrobicupola and biaugmented triangular prism
		15 triangles: triaugmented dodecahedron, diminished rhombicosidodecahedron, paragyrate diminished rhombicosidodecahedron, metagyrate diminished rhombicosidodecahedron, bigyrate diminished rhombicosidodecahedron, gyroelongated pentagonal pyramid, pentagonal orthocupolarontunda, pentagonal gyrocupolarotunda, elongated pentagonal orthocupolarotunda and elongated pentagonal gyrocupolarotunda
	polyhedra.org /poly/polygon/3/triangle (396 words)

	Pentagonal Dipyramid -- from Wolfram MathWorld
		The pentagonal dipyramid is one of the convex deltahedra, and Johnson solid
		A pentagonal dipyramid appears in the lower left as one of the polyhedral "stars" in M. Escher's 1948 wood engraving "Stars" (Forty 2003, Plate 43).
		For a pentagonal dipyramid having a base with unit edge lengths, the circumradius of the base pentagon is
	mathworld.wolfram.com /PentagonalDipyramid.html (151 words)

	Polyhedron, Polyhedra, Polytopes - Numericana
		A number known as the golden ratio, which happens to be the ratio of the diagonal to the side in a regular pentagon.
		dipyramid becomes if you twist its upper pyramidal cone 1/2n of a turn with respect to the lower one: The intersection of the two cones becomes a solid whose faces are quadrilaterals [see figure at right].
		Each n-gonal pyramid consists of n slices (as pictured at left) sharing an edge from O to the center M of the n-gon (n is 5 or 6).
	home.att.net /~numericana/answer/polyhedra.htm (5442 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 most regular solid with seven vertices is a pentagonal dipyramid.
		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)

	Elongated dipyramid at AllExperts
		In geometry, the elongated dipyramids are an infinite set of polyhedra, constructed by elongating an n'-agonal bipyramid (by inserting an n-agonal prism between its congruent halves.
		There are three elongated dipyramids'' that are Johnson solids made from regular triangles and squares.
		* Elongated pentagonal dipyramid (J16) - 10 triangles, 5 squares - dual Pentagonal bifrustum
	en.allexperts.com /e/e/el/elongated_dipyramid.htm (191 words)

	Pyramids, dipyramids, and trapezohedra (Site not responding. Last check: 2007-10-20)
		Joining two such pyramids at their bases gives a set of three dipyramids, in which all faces are equilateral triangles: the triangular dipyramid, the octahedron (square dipyramid), and the pentagonal dipyramid.
		As an example, here is the compound of the hexagonal prism and its dual hexagonal dipyramid, clearly showing their dual relationship and the fact that the triangles are not equilateral.
		Parallel to the prisms and their dual dipyramids, there is an infinite series of antiprisms and their duals, called trapezohedra.
	www.georgehart.com /virtual-polyhedra/pyramids-info.html (299 words)

	Body Solid -- Recommendations and Resources (Site not responding. Last check: 2007-10-20)
		The names and Johnson numbers for the solids are: #square pyramid #pentagonal pyramid #triangular cupola #square cupola #pentagonal cupola #pentagonal rotunda #elongated triangular pyramid #elongated square pyramid #elongated pentagonal pyramid #gyroelongated square pyramid #gyroelongated pentagonal pyramid #triangular dipyramid #pentagonal dipyramid #elongated triangular dipyramid #elongated square dipyramid #elongated pentagonal dipyramid #gyroelongated square dipyramid
		And for: #*Triangular faces: each vertex of a regular triangle is 60°, so a shape should be possible with 3, 4, or 5 triangles meeting at a vertex; these are the tetrahedron, octahedron, and icosahedron respectively.
		*#Pentagonal** faces: each vertex is 108°; again, only one arrangement, of three faces at a vertex is possible, the dodecahedron.
	www.becomingapediatrician.com /health/20/body-solid.html (2061 words)

	Puzzle Pieces... (Site not responding. Last check: 2007-10-20)
		A pentagonal dipyramid with a single strip of 31 equilateral triangles.
		A triangular dipyramid with a single strip of 19 equilateral triangles.
		An analogous construction may be made for the triangular dipyramid shown in Figure 5(c).
	www.mi.sanu.ac.yu /vismath/hil/pe3.htm (2740 words)

	[No title]
		I drew a diagram of the pentagonal dipyramid and labeled each vertex to facilitate discussion and show how to communicate using pictures and labels.
		The pentagonal dipyramid and boat had examples of non-obvious rotations.
		The boat was examined using masking tape for each mirror plane and it was observed that the axis of rotation passed through the points where the tapes cross.
	www.math.umn.edu /~morgan/Classdiary.doc (3503 words)

	Elongated pentagonal dipyramid at AllExperts
		In geometry, the elongated pentagonal dipyramid is one of the Johnson solids (J
		) by inserting a pentagonal prism between its congruent halves.
		The 92 Johnson solids were named and described by Norman Johnson in 1966.
	en.allexperts.com /e/e/el/elongated_pentagonal_dipyramid.htm (124 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.
		5.2 There are only five convex deltahedra: triangular dipyramid, pentagonal dipyramid, 12-faced deltahedron, 14-faced deltahedron, 16-faced deltahedron excluding the Platonic polyhedra: tetrahedron, octahedron, icosahedron).
		There is an infinite number of concave deltahedra...However, there are only eight convex deltahedra: tetrahedron, octahedron, icosahedron, triangular dipyramid, pentagonal dipyramid, 12-faced deltahedron, 14-faced deltahedron, 16-faced deltahedron.
	www.laetusinpraesens.org /docs80s/84nsetsx/x18.php (1214 words)

	Download Poly (16-bit) v1.05 Shareware software - Softlookup Downloads (Site not responding. Last check: 2007-10-20)
		Poly enbles you to manipulate a polyhedral solid and print out a flattened version, which can be cut out, folded, and taped to produce a three-dimensional model.
		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).
	www.softlookup.com /display.asp?id=16053 (286 words)

	vizualization vs. verbalization (Site not responding. Last check: 2007-10-20)
		which is also a dipyramid is not included here because it is mentioned above).
		This solid can be thought of as a Tetrahedron split into two wedges each made of two adjacent faces, which are then joined together by a band of eight triangles.
		- Gyroelongated square dipyramid - two square pyramids attached to a square antiprism [1].
	www.mi.sanu.ac.yu /vismath/wertheim/visualization4.HTM (312 words)

	Pentagonal Prism (Site not responding. Last check: 2007-10-20)
		Home > Gallery > My Models > Prisms > Pentagonal Prism.
		I managed to fit all the yellow nets for the pentagonal prism, pentagonal antiprism, and pentagrammic prism all on one page.
		The top and bottom polygon of each model was printed separately on different coloured paper.
	web.aanet.com.au /robertw/Prism5.html (94 words)

	Tom Gettys - Deltahedra (Site not responding. Last check: 2007-10-20)
		Let us now investigate what convex polyhedra result if we relax the requirement that every vertex be identical.
		In the article on the Platonic Solids we realized that there is only one convex polyhedron with all square faces (the Cube), and only one convex polyhedron with all pentagonal faces (the Dodecahedron).
		Using equilateral triangles for the faces, however, we found 3 convex polyhedrons: the Tetrahedron, Octahedron and Icosahedron.
	home.comcast.net /~tpgettys/delta.html (453 words)

	Untitled Document
		Just like their dual Archimedean partners there are two chiral Catalan solids: the pentagonal icositetrahedron and the pentagonal hexecontahedron.
		Named after Normal W. Johnson who was the first to catalogue them in 1966.
		PNY Pentagonal Pyramid 5 isosceles tri, 1 pent Pyramid
	www.artangent.com /sygma.htm (488 words)

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