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Topic: Stellation

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	Stellations
		For example, the first stellation of the cuboctahedron is the compound of the cube and octahedron.
		The first stellation of the icosidodecahedron is the compound of the icosahedron and the dodecahedron.
		The third stellation can be seen as a compound of six tetragonal disphenoids, very similar to the rigid compound of 6 tetrahedra; again only a slight change in triangle shape from equilateral is necessary to obtain the stellated rhombic dodecahedron.
	www.georgehart.com /virtual-polyhedra/stellations-info.html (549 words)

	Stellating and facetting - a brief history
		Stellation is the process of extending the sides of a polygon, the faces of a polyhedron, and generally the cells of a higher-dimensional polytope, until they meet to form a new figure.
		Luke examines the stellations of the rhombic dodecahedron.
		Luke, Stellations of the rhombic dodecahedron, The Mathematical Gazette 41 (1957), pp.
	www.steelpillow.com /polyhedra/StelFacet/history.html (1879 words)

	Stellation with Java3D (Site not responding. Last check: 2007-11-06)
		Stellating a polygon or polyhedron creates a family of new shapes from the original shape, sometimes much more beautiful and intricate.
		Stellation is a process of extending the faces of a polyhedron to create a larger one.
		This a stellation diagram; the triangle in the middle of this figure represents the original triangular face of the icosahedron, and surrounding it are three other shapes that lie in the plane of that face.
	www.cacr.caltech.edu /~roy/Stellate/explain.html (529 words)

	Stella: Polyhedron Navigator
		The stellation diagram (see figure 6) is a two-dimensional diagram that lies in the same plane as one of the faces of the original polyhedron, and shows a line for each intersection with one of the other face planes.
		The stellation diagram may be viewed flat in its own window, or displayed in 3D perspective attached to one of the faces of the original or stellated model, which gives the user a good feel for what the stellation diagram is all about.
		As with the stellation diagram, some cells in the cell diagram can be filled to indicate their inclusion in a stellation, thus the cell diagram is also a convenient way to represent any particular stellation (the shading in figure 7 corresponds to the same stellations as in figure 6).
	home.aanet.com.au /robertw/PolyNav/PolyNavigator.html (12506 words)

	An Interactive Creation of Polyhedra Stellations with various Symmetries (Site not responding. Last check: 2007-11-06)
		We call a stellation subcell of symmetry H an array of elementary stellation cells which is invariant under operations of subgroup H.
		The complete stellation cell, formed by an array of elementary cells is shown in Fig.15 (stellation e1 from [2]).
		The stellations applet [11] was written to greatly facilitate the process of stellation construction.
	www.mi.sanu.ac.yu /vismath/bulatov (2287 words)

	Stellation - Wikipedia, the free encyclopedia
		Stellation is a process of constructing new polygons (in two dimensions), new polyhedra in three dimensions, or, in general, new polytopes in n dimensions.
		A sub-symmetric stellation is one where not all elements are extended symmetrically.
		A stellation of a regular polygon is a star polygon or polygon compound.
	en.wikipedia.org /wiki/Stellation (1096 words)

	Stellating a convex hull - M. Fleurent (Site not responding. Last check: 2007-11-06)
		Stellation Diagram 1 - Stellations of the Icosahedron
		The two stellation diagrams of the convex hull (“CV”) of the final stellation of the icosahedron are closely related to the stellation diagrams of the icosahedron and the dodecahedron.
		The stellation diagram of the dodecahedron is embedded in the second stellation diagram of CV.
	users.skynet.be /polyhedra.fleurent/Stellations/Convex_hull/Convex_hull.htm (577 words)

	Stellated Polyhedra
		Below is a set of seven stellations of the pentagonal icositetrahedron, dual of the snub cube.
		By stellating the pentagonal hexecontahedron, dual of the snub dodecahedron, you could also create dodecahedral and icosahedral variants on this same idea.
		Yes, that would be a sub-symmetric stellation of the dodecahedron, dual of the icosahedron, which may be thought of as a snub tetrahedron.
	web.aanet.com.au /robertw/Stellations.html (394 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Stellation CM manages and versions small artifacts, such as method declarations, instead of entire source files.
		Through the use of a query language, Stellation allows programmers to dynamically generated new virtual source files allowing programmers to manipulate multiple viewpoints on the same code.
		Stellation allows programmers to create a heirarchy of repository replicas, allowing programmers to match coordination structure to the structure of their team.
	domino.research.ibm.com /synedra/synedra.nsf/Stellation-CM?OpenPage (190 words)

	Tidy icosahedra and dodecahedra
		This is the third in a series of papers attempting to revisit the stellations of the regular icosahedron and their duals, the facettings of the regular dodecahedron.
		The analyses of stellations according to cell aggregates or surhedra are unable to distinguish between these polyhedra, or to explain the existence of two uniform reciprocals, and are clearly seen to be inadequate.
		The fully supported stellations include a number of more basic types, such as the primary, mainline and monoacral stellations [7], so we have also gained some insight into these types; the limitations of the associated analyses in terms of cell aggregates or surhedra are evident.
	www.steelpillow.com /polyhedra/icosa/tidystelfacet/TidyStelFacet.htm (3018 words)

	Stellation
		Stellation is a process to construct new polygons (in two dimensions) and to construct new polyhedra in three dimensions.
		The process consist in extending the facial planes until they meet each other.
		The resulting polyhedron is the new stellated polyhedron.
	www.ebroadcast.com.au /lookup/encyclopedia/st/Stellation.html (40 words)

	Javangelist :: Stellation
		While Stellation provides all of the standard functions available in any SCM system, it is distinguished by a number of advanced features, such as project-oriented versioning and lightweight branching, intended to ease the development of software systems by large groups of loosely coordinated developers.
		We intend for Stellation to become not only a highly-effective SCM system for general software development, but also a platform for research on tools and systems that exploit fine-grained management of software artifacts, such as dynamic program organization, inter-programmer and inter-group communication and coordination, and UI mechanisms that effectively make use of these capabilities.
		Stellation currently provides both a set of Eclipse plugins for using Stellation as a Team provider for Eclipse, and a command line tool for using Stellation as a standalone SCM system.
	www.javangelist.de /space/Stellation (194 words)

	Stellations of the Cuboctahedron (Site not responding. Last check: 2007-11-06)
		The simplest stellation (other than the "zeroth stellation" which is the cuboctahedron itself) is the compound of the cube and octahedron, illustrated at right.
		The intersection of the cube and the octahedron is the inner cuboctahedron.
		The stella octangula comes from stellating the triangular faces of the cuboctahedron, and the dimples are carved in the planes of the square faces.
	www.georgehart.com /virtual-polyhedra/stellations-cuboctahedron.html (199 words)

	book outline (Site not responding. Last check: 2007-11-06)
		An Introduction to Stellation Theory is meant to be an introduction to the theory of stellations of polyhedra.
		In this section, stellations for all of the Archimedean solids and their duals are given.
		In this section, the stellations of a series of irregular pentagonal dodecahedra and their dual icosahedra are discussed.
	websites.quincy.edu /~matskvi/stellbook.html (770 words)

	Stellations of Polyhedra (Site not responding. Last check: 2007-11-06)
		Below are shown stellations of the tetrahedron, cube, octahedron, pentagonal dodecahedron and rhombic dodecahedron.
		Stellations of the icosahedron are much more complex and shown on separate pages.
		This is obtained by continuing the star planes of the small stellated dodecahedron outward until they meet to form the next set of pentagons.
	www.uwgb.edu /dutchs/symmetry/stellate.htm (325 words)

	Stellation
		One of Stellation's main differences is that it features real geography; a galaxy of about a hundred (currently) stars on a 2D grid.
		If you want to see how it works, want to set up your own Stellation server, or feel like fixing something you think is broken, this is the place to go.
		Stellation has two types of units; mobile units and stationary units.
	stellation.sourceforge.net (1089 words)

	Cardboard Models by G.M. Fleurent (Site not responding. Last check: 2007-11-06)
		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.
		This stellation is not a compound, thereafter there is not a left- or right constituent.
	users.skynet.be /polyhedra.fleurent/Stellations/Cardboard_Models.htm (282 words)

	Tom Gettys - Stellated Solids (Site not responding. Last check: 2007-11-06)
		Stellation is a process that allows us to derive a new polyhedron from an existing one by extending the faces until they re-intersect.
		This is the second stellation of the Octagon.
		Here are a couple of exercises for you: First, convince yourself that the Triangle and Square have no stellations, that the Pentagon and Hexagon have one stellation, and that the Heptagon and Octagon have two stellations.
	home.comcast.net /~tpgettys/stellate.html (436 words)

	Completion, Stellation, and Faceting (Site not responding. Last check: 2007-11-06)
		Three primitive functions or operations are defined and compared: completion, stellation, and faceting.
		In stellation, the sides of the 17-gon are produced, until they intersect in new vertices.
		For instance, there are many million different stellations of Kepler's Rhombic Triacontahedron; and the entire series of zonohedral completions has not yet even been worked out for the Archimedean solids.
	users.neworld.net /~rtowle/Polytopes/Primitive/primitives.html (431 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		The Stellation project at IBM Research is working on developing programming environments that support collaboration between members of programming teams.
		Stellation was formerly known by the names Synedra and Coven.
		In the long term, our goal is to fundamentally change the way that people program, by creating a new model of software development that allows people to collaborate more effectively.
	domino.research.ibm.com /synedra/synedra.nsf (77 words)

	Icosahedral precursors
		As is usual, we distinguish between compound polyhedra and compound stellations or facettings as follows.
		The face diagram of a stellation may be represented by an anticlockwise circuit around the figure, noting the sequence of vertices and edges traversed.
		The face of a stellation is thus uniquely identified by a sequence of letters.
	www.steelpillow.com /polyhedra/icosa/icosagen/IcosaGen.htm (3070 words)

	Stellations of the Icosahedron (Site not responding. Last check: 2007-11-06)
		In levels E-G, it is possible to have stellations that expose the interior faces of the cells.
		Many of the g-cell stellations are all but indistinguishable from the outside and differ only in the form of their interior tunnels.
		Some other g-cell stellations can be viewed as an outer shell of g-cells enclosing and touching some simpler stellation, and new views of some of these stellations are presented here.
	www.uwgb.edu /dutchs/symmetry/stelicos.htm (352 words)

	ALS TDF
		Cultured rat cortical astrocytes exhibited flattened, polygonal morphology in the absence of stimulation, but differentiated into process-bearing stellate cells in response to the membrane-permeable cyclic AMP analog dibutyryl cyclic AMP (dBcAMP) or the protein kinase C (PKC) activator phorbol 12-myristate 13-acetate (PMA).
		The PMA-induced astrocyte stellation and ERK1/2 phosphorylation were blocked by specific PKC inhibitors, GF-109203X (0.01-1 microM) and calphostin C (1 microM).
		These results suggest that the MEK/ERK cascade is involved in the induction and maintenance of astrocyte stellation mediated by PKC, but not by cyclic AMP signaling.
	www.als.net /articles/articleDetail.asp?articleID=2470 (241 words)

	stellated / stellation - procedure whereby the generating n-ad is completed at partial chord or "facet" of a CPS
		stellated / stellation - procedure whereby the generating n-ad is completed at partial chord or "facet" of a CPS
		Synonyms of the Stellated Hexany are Mandala, Tetradekany, and Dekatesserany.
		When tetrachords are used as generators, the resulting scale is an aggregate of original and inverted tetrachords in novel pitch relationships.
	tonalsoft.com /enc/s/stellated.aspx (285 words)

	Graphics Archive - DodecaFoam! Third Stellation by Chaim ... (Site not responding. Last check: 2007-11-06)
		The recipe for filling a large dodecahedron with small dodecas involves examing the three stellations of the dodecahedron.
		Here, the third stellation of the dodecahedron is filled with tiny dodecas.
		Note the vertices of this figure lie on the vertices of a large dodecahedron.
	www.geom.uiuc.edu /graphics/pix/Special_Topics/Tilings/third_stell.html (159 words)

	Bill Richter's Home Page (Site not responding. Last check: 2007-11-06)
		The picture illustrates that the golden mean is ratio of diagonal of a pentagon to a side.
		Note that the 1st stellation looks quite different from the Mathematica icon.
		A 5-pointed star is the simplest example of a stellation (of a pentagon).
	www.math.northwestern.edu /~richter (312 words)

	Permutated Third Stellation
		The six dissimilar pieces of this puzzle are anologous to those of the Second Stellation.
		In The Puzzling World Of Polyhedral Dissections the Second Stellation is called the Purmutated Second Stellation.
		For example, some of his puzzles with the second stellation shape were called Nova and Super Nova.
	www.johnrausch.com /puzzleWorld/puz/permutated_third_stellation.htm (168 words)

	Open Source Xara Xtreme - All about QuickShapes
		These are the primary and stellation points, and the points along the edges of the shape where the curvature points join the edge path.
		If the shape is stellated then the stellation edge path is transmogrified to lie along that edge.
		These three tools are derived from one base class that implements all of the common code (which is most of the code in the three tools).
	www.xaraxtreme.org /developers/documentation/all_about_quickshapes.html (1570 words)

	Stellation of Small Stellated Truncated Dodecahedron
		The model is a stellation of the small stellated truncated dodecahedron, pictured here, which should probably really be called the truncated small stellated dodecahedron.
		This shows one of the two types of faces, from the pentagon plane of the small stellated truncated dodecahedron.
		This shows the other type of face, from the decagram plane of the small stellated truncated dodecahedron.
	web.aanet.com.au /robertw/StelSSTD.html (336 words)

	cancer stellation (Site not responding. Last check: 2007-11-06)
		I would have been A blank the cancer stellation web and if the motif which is a reduction of a suitably.Those the advertisers, is to reply to do, for that even thoseinvolved.
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		can: be assured of slowing Dollars with cancer stellation gov: ernment D h, z C, o cli ck He g.
	cancer-stellation.b17.startrekexcelsior.com (254 words)

	Stellations of the Dodecahedron
		The edges and vertices of the dodecahedron occur on intersections of these planes.
		The stellation process works because the 12 planes have additional intersections outside of the core dodecahedron (it wouldn't work for a cube).
		We stellate a polyhedron by extending all its faces until they intersect again along new edges.
	dogfeathers.com /java/stardodec.html (730 words)

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