
	Where results make sense

Topic: Pentagonal icositetrahedron

In the News (Wed 15 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Crystallography - LoveToKnow 1911
		pentagons, and although similar to each other they are respectively rightand left-handed, one being the mirror image of the other; such similar but nonsuperposable forms are said to be enantiomorphous (iv avrios, opposite, and,uopon, form), and crystals showing such forms sometimes rotate the plane of polarization of plane-polarized light.
		Faces of a pentagonal icositetrahedron with high indices have been very rarely observed on crystals of cuprite, potassium chloride and ammonium chloride, but none of these are circular polarizing.
		This is bounded by twelve irregular pentagons, and is a tetartohedral or quarter-faced form of the hexakis-octahedron.
	www.1911encyclopedia.org /Crystallography (14968 words)

	[No title]
		pentagonal icositetrahedron +------------------------------------------------------------ The pentagonal icositetrahedron is a polyhedron with 38 vertices and 24 faces.
		pentagonal dipyramid +------------------------------------------------------------ The pentagonal dipyramid is a polyhedron with 7 vertices and 10 faces.
		pentagonal gyrobicupola +------------------------------------------------------------ The pentagonal gyrobicupola is a polyhedron with 20 vertices and 22 faces.
	www.math.harvard.edu /~knill/sofia/data/polyhedra.txt (2272 words)

	Cuprite - LoveToKnow 1911
		Well-developed crystals are of common occurrence; they usually have the form of the regular octahedron, sometimes in combination with the cube and the rhombic dodecahedron.
		A few Cornish crystals have been observed with faces of a form {hkl} known as the pentagonal icositetrahedron, since it is bounded by twenty-four irregular pentagons.
		In this class of cubic crystals there are no planes or centre of symmetry, but the full number (thirteen) of axes of symmetry; it is known as the trapezohedral hemihedral class, and cuprite affords the best example of this type of symmetry.
	www.1911encyclopedia.org /Cuprite (513 words)

	CRYSTALLOGRAPHY - LoveToKnow Article on CRYSTALLOGRAPHY (Site not responding. Last check: 2007-10-24)
		pentagons, and althnugh similar to each other they are respectivel right- and left-handed, one being the mirror image of the other; soc similar but nonsuperposable forms are said to be enantiomorphous (~vavrtoi, opposite, and uop~, form), and crystals showing such forms sometimes rotate the plane of polarization of plane-polarized light.
		Faces of a pentagonal icositetrahedron with high indices have been very rarely observed on crystals of cuprite, potassium chloride and ammonium chloride, but none of these are circular polarizing.
		In the thermo-electrically positive crystals of pyrites the faces of the pentagonal dodecahedron are striated parallel to the cubic edges, whilst in the rarer negative crystals the faces are striated perpendicular to these edges.
	41.1911encyclopedia.org /C/CR/CRYSTALLOGRAPHY.htm (20186 words)

	Poliedri
		The design is harmonious and rhythmical, consisting of twelve pentagonal stars, each composed of five rhombs totally overlapping each other, in such a way that the twelve pentagonal stars wrap exactly two times the surface of the rhombic triacontahedron.
		This principle is clearly visible at the center figures of the two preceding plates, where the length of the sides of trigonal pyramids correspond to the height of the tetragonal and pentagonal pyramids.
		The solid laevo pentagonal hexecontahedron is obtained by the application of several consecutive geometric operations constructed on the surface of the dextro snub dodecahedron (lower figure in the plate), which is the archetype of the pentagonal hexecontahedron.
	www.gicas.net /poliedri_text.html (4932 words)

	Multidimensional Glossary
		An altered pentagonal prism is a pentagrammatic antiprism.
		For example, joining identical pentagonal pyramids of altitude approximately +1.3764 to two opposite faces of a unit regular dodecahedron produces a pentagonal antibipyramid, whose symmetry group is a subgroup of the symmetry group of the dodecahedron.
		It is the former that is the dual of the hollow pentagon.
	members.aol.com /Polycell/glossary.html (16070 words)

	PLAGIHEDRALI CLASS - Online Information article about PLAGIHEDRALI CLASS
		octahedron two pentagonal icositetrahedra {hkl) and (khl) are derived.
		These are each bounded by twenty-four irregular Icositetrahedron.
		Faces of a pentagonal icositetrahedron with high indices have been very rarely observed on crystals of See also:
	encyclopedia.jrank.org /PIG_POL/PLAGIHEDRALI_CLASS.html (286 words)

	CUPRITE - LoveToKnow Article on CUPRITE (Site not responding. Last check: 2007-10-24)
		Well-developed crystals are of common occurrence; they usually have the form of the regular octahedron, sometimes in combination with the.cube and the rhombic dodecahedron.
		A few Cornish crystals have been observed with faces of a form {hkl} known as the pentagonal icositetrahedron, since it is bounded by twenty-four irregular pentagons.
		In this class of cubic crystals there are no planes or centre of symmetry, but the full number (thirteen) of axes of symmetry; it is known as the trapezohedral hemihedral class, and cuprite affords the best example of this type of symmetry.
	48.1911encyclopedia.org /C/CU/CUPRITE.htm (480 words)

	Properties of Dice
		While we require that all the faces on the dice are equivalent, the same is not true for the vertices.
		In the cases 2 < M < 6, unless all the corners are equivalent, the only rotational symmetry is for a 180 degree rotation: There isn't room in a quadrangle for three-way symmetry, or in a pentagon for three-way or four-way symmetry.
		For pentagons, we find two possible combinations: 2 doublets plus 1 singlet (with one doublet being the corners on either side of the singlet, and the other doublet being the remaining two corners), and 5 singlets.
	www.fantasylibrary.com /lounge/diceprop.htm (3085 words)

	Transpolyhedra (Site not responding. Last check: 2007-10-24)
		trans snub cube --- transforms between a snub cube and its dual pentagonal icositetrahedron.
		trans pentagonal prism --- transforms between a pentagonal prism and its dual pentagonal dipyramid.
		trans pentagonal antiprism --- transforms between a pentagonal antiprism and its dual pentagonal trapezohedron.
	euch3i.chem.emory.edu /proposal/www.li.net/~george/virtual-polyhedra/transpolyhedra.html (562 words)

	Stars (M. C. Escher) - Open Encyclopedia (Site not responding. Last check: 2007-10-24)
		A deltoidal icositetrahedron appears in the middle right.
		A pentagonal dipyramid appears in the lower left.
		A cube-octahedron compound appears in the upper left.
	www.open-encyclopedia.com /Stars_%28M._C._Escher%29 (193 words)

	Transpolyhedra
		trans snub cube --- transforms between a snub cube and its dual pentagonal icositetrahedron.
		trans pentagonal prism --- transforms between a pentagonal prism and its dual pentagonal dipyramid.
		trans pentagonal antiprism --- transforms between a pentagonal antiprism and its dual pentagonal trapezohedron.
	www.georgehart.com /virtual-polyhedra/transpolyhedra.html (505 words)

	Computer Graphics - Available Polyhedrons
		Icosidodecahedron (12 pentagons, 20 triangles; dual of the Rhombic triacontahedron)
		Pentagonal Icositetrahedron (24 pentagons; dual of the Snub Cube)
		Pentagonal Hexecontahedron (60 pentagons; dual of the Snub Dodecahedron; especially difficult)
	www.soi.city.ac.uk /~dcd/ig/cwk/pol.htm (500 words)

	The International Bone Rollers' Guild
		The Pentagonal Icositetrahedron (left) is dual to the Snub Cube.
		Its twenty-four irregular pentagonal faces are arranged in a matter suggesting its relationship to the Hexahedron and Octahedron.
		Likewise, the Pentagonal Hexecontahedron (left) is comprised of irregular pentagons.
	members.aol.com /dicetalk/polyh5.htm (282 words)

	Polyhedra Names
		A pentakis dodecahedron is based on the dodecahedron, but each pentagon is replaced with five isosceles triangles.
		Numerical modifiers like pentagonal or hexagonal can refer not only to the shape of individual faces, but also to a base polygon from which certain infinite series of special polyhedra can be constructed.
		For example the pentagonal prism and hexagonal prism are two members of an infinite series.
	www.georgehart.com /virtual-polyhedra/naming.html (1134 words)

	Stellations : Introduction - G.M. Fleurent
		Robert Webb mentions 5 chiral monohedral stellations of the Pentagonal Icositetrahedron (dual to the Snub Cube).
		The 9 lines of symmetry in the asymmetrical "extended" stellation diagram of the Pentagonal Icositetrahedron form 14 regions, excluding the central region.
		The core of the dual of the Truncated Cuboctahedron, the Disdyakisdodecahedron is very similar to the core of the extended stellation diagram of the Pentagonal Icositetrahedron.
	users.skynet.be /polyhedra.fleurent/Stellations/Introduction.htm (1377 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.
		The icosidodecahedron could also be called a pentagonal gyrobirotunda but that name would masks its much greater symmetry compared to the related pentagonal orthobirotunda (J34).
		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)

	Pentagonal Icositetrahedron (Site not responding. Last check: 2007-10-24)
		So an icosagon is an 20 sided shape and an icosahedron is a 20 faced shape.
		Below are the main properties of the Pentagonal Icositetrahedron:
		If you would like to view the net for this shape please click on the picture above.
	home.btconnect.com /shapemakingclub/shapenets/32pentagonalicositetrahedron.html (69 words)

	Snub Cube (Site not responding. Last check: 2007-10-24)
		The snub cube has 24 vertices, 60 edges and 38 facets, 6 squares and 32 triangles.
		It is one of the thirteen Archimedean solids and its dual is called pentagonal icositetrahedron.
		Maybe the first presentation of this polytope can be found in the revised version of Albrecht Dürer's Underweysung der Messung (around 1538).
	www.eg-models.de /models/Discrete_Mathematics/Lattices_and_Packings/Densest_Polytopes/2001.02.059/_preview.html (179 words)

	Near Misses (Site not responding. Last check: 2007-10-24)
		I(1,2,,[2]): 12 pentagons*, 20 hexagons, 60 almost equilateral triangles.
		One imagines that by fiddling with it a bit, one could sacrifice the perfect regularity of the decagons and dodecagons in exchange for eliminating the narrow rectangular faces, resulting in a near miss.
		A solid constructed by inscribing a regular 11-gon in every face of a pentagonal icositetrahedron.
	www.cgl.uwaterloo.ca /~csk/projects/nearmisses (237 words)

	Pentagonal icositetrahedron -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-24)
		Pentagonal icositetrahedron -- Facts, Info, and Encyclopedia article
		(additional info and facts about irregular pentagon) irregular pentagon
		A pentagonal icositetrahedron is a (additional info and facts about catalan solid) catalan solid which looks a bit like an (Any polyhedron having eight plane faces) octahedron undergoing (The process in reproduction and growth by which a cell divides to form daughter cells) cell division.
	www.absoluteastronomy.com /encyclopedia/P/Pe/Pentagonal_icositetrahedron.htm (104 words)

	Rarer variations - Dice (Site not responding. Last check: 2007-10-24)
		When landing on an edge, the topmost edge has pips for 1 through 5.
		The pentagonal faces are labeled with the digits 6 and 7.
		Such dice are used in a seven-player variant of backgammon.
	games.dice.en.exsugo.org /Rarer%20variations.htm (371 words)

	subendospheric polyhedra
		The Subendosphaerica gyroidea are based on geometric bodies called Gyroids or Pentagonal Icositetrahedra.
		The Subendosphaerica pyritoidea are based on geometric bodies called Pyritohedra or Pentagonal Dodecahedra.
		The Subendosphaerica tetartoidea are based on geometric bodies called Tetartoids or Tetrahedral Pentagonal Dodecahedra.
	home.hetnet.nl /~turing/subendospheric.html (534 words)

	Stellation of Pentagonal Icositetrahedron 5 (Site not responding. Last check: 2007-10-24)
		Home > Gallery > My Models > Stellated Polyhedra > Stellation of Pentagonal Icositetrahedron 5.
		A stellation of the pentagonal icositetrahedron, dual of the snub cube.
		In the stellation diagram, the red regions make up the faces of the model, and the green regions are internal to the model.
	home.aanet.com.au /robertw/PIStel5.html (74 words)

	Archimedean Duals (Site not responding. Last check: 2007-10-24)
		The relationships between the Archimedean solids and their respective duals is nicely brought out by studying a compound of a solid and its dual.
		For example, the snub cube and its dual, the pentagonal icositetrahedron, combine into this beautiful compound.
		The five-sided faces of the dual correspond to the fact that five polygons (four triangles and a square) meet at each vertex of the snub cube.
	www.georgehart.com /virtual-polyhedra/archimedean-duals-info.html (436 words)

	Amazon.com All Products Search Results (Site not responding. Last check: 2007-10-24)
		Click here to see additional results that may be relevant to your search.
		It is also called the trapezoidal icositetrahedron (Holden 1971, p.
		A deltoidal icositetrahedron appears in the middle right as one of the polyhedral...
	www.independentcommerce.com /icDirectory/keyword.asp?keyword=icositetrahedron (127 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-24)
		John Conway ______________________________________________ From: "John Conway" Subject: Re: 11-gon Date: Mon, 24 Oct 94 21:21:28 EDT By the way, "icositetrahedron" appears in some dictionaries.
		The dual of the rhombicuboctahedron has been called either a trapezoidal or tetragonal icositetrahedron, while the dual of the snub cube is a pentagonal icositetrahedron.
		I saw the word "tetrakaidecahedron" in a recent "press release" from the Minneapolis Geometry Center, so you can see that people DO occasionally use such words.
	www.mathforum.org /dr.math/problems/naming.polygons.html (841 words)

	Cardboard Models by G.M. Fleurent (Site not responding. Last check: 2007-10-24)
		If a face passes through the centre of the reciprocating sphere, then the corresponding vertex of the dual is located at infinity and the connecting edges describe an infinitely long prism."
		My favourite stellation diagram is the one of the Pentagonal Icositetrahedron, the dual of the Snub Cube.
		I have drawn in 1982 the stellation patterns of the final stellation for both: a pattern without lines prolonged at infinity, a pattern with parallel lines prolonged at infinity.
	users.skynet.be /polyhedra.fleurent/Stellations/Cardboard_Models.htm (282 words)

	The Archimedean Dual, Table of Contents (Site not responding. Last check: 2007-10-24)
		Angles, Dimensions, and ratios of proportion for the pentagon
		Do is two, deca is ten, and hedra is bases, so a dodecahedron is two and ten pentagons inscribed in a sphere.
		Dodecahedron, 12 pentagons inscribed in a sphere, top, front, and side view.
	www.thearchimedeandual.com /Table_of_Contents.htm (4948 words)

	Promorphology of Crystals I
		The geometric solid taken (according to the above established criteria) to represent the stereometric basic form (promorph) of all the crystals of this Class is the Gyroid or Pentagonal Icositetrahedron (Figure 5).
		The geometric solid taken (according to the above established criteria) to represent the stereometric basic form (promorph) of all the crystals of this Class is the Pyritohedron or Pentagonal Dodecahedron (Figure 6).
		Pyritohedron or Pentagonal Dodecahedron, Stereometric Basic Form of all the (single) crystals of the Duakisdodecahedric Class of the Isometric Crystal System.
	home.hetnet.nl /~turing/promorph_crystals.html (4016 words)

	P214: Computer Graphics 1 - Coursework Groups
		Snub Dodecahedron (12 pentagons, 80 triangles; - looks VERY difficult)
		Pentagonal Icositetrahedron (24 pentagons; dual of the Snub Cube; looks VERY difficult)
		Pentagonal Hexecontahedron (60 pentagons; dual of the Snub Dodecahedron; looks VERY difficult)
	www.soi.city.ac.uk /~dcd/ig2/groups.htm (297 words)

	[No title]
		비틀어 늘린 맞붙인 두 오각지붕 (Gyroelongated Pentagonal Bicupola) (J46)
		비틀어 늘린 맞붙인 오각지붕과 오각둥근지붕 (Gyroelongated Pentagonal Cupolarotunda) (J47)
		비틀어 늘린 맞붙인 두 오각둥근지붕 (Gyroelongated Pentagonal Birotunda) (J48)
	www.mathlove.co.kr /sw/Poly/Poly-polyhedra.htm (872 words)

Try your search on: Qwika (all wikis)