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Topic: Pentachoron

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	Pentachoron - Wikipedia, the free encyclopedia
		The pentachoron, also called a pentatope or 4-simplex, is the simplest convex regular polychoron (a type of four-dimensional geometric figure).
		The pentachoron consists of five cells, all tetrahedra, and is self-dual.
		The closest or farthest vertex of the pentachoron, respectively, projects to the center of the tetrahedron.
	en.wikipedia.org /wiki/Pentachoron (204 words)

	Triangular Rectates (Site not responding. Last check: 2007-10-20)
		(rectified pentachoron) - cells are 5 tets and 5 octs, has 3P verf (vertex figure).
		(facetorectified pentachoron) - cells are 5 tets and 10 trips, has 3/2 AP verf (AP = antiprism).
		(prismatointercepted pentachoron) - cells are 5 octs and 10 trips, has inverted 3P verf.
	members.aol.com /hedrondude/rectates.html (425 words)

	pentachoron - OneLook Dictionary Search (Site not responding. Last check: 2007-10-20)
		We found 2 dictionaries with English definitions that include the word pentachoron:
		Tip: Click on the first link on a line below to go directly to a page where "pentachoron" is defined.
		Pentachoron : Eric Weisstein's World of Mathematics [home, info]
	www.onelook.com /?w=pentachoron (77 words)

	Nomenclature (Site not responding. Last check: 2007-10-20)
		Just as the five Platonic polyhedra are “basal” to naming the 13 nonprismatic Archimedean polyhedra, so are the six regular polychora basal to naming the 40 nonprismatic Archimedean polychora.
		The six regular polychora I call the pentachoron (with 5 tetrahedral cells), tesseract (with 8 cubic cells), hexadecachoron (with 16 tetrahedral cells), icositetrachoron (with 24 octahedral cells), hecatonicosachoron (with 120 dodecahedral cells), and hexacosichoron (with 600 tetrahedral cells).
		For example, the Bowers name for the dispentachoron is rap, short for rectified pentachoron, which is Norman Johnson’s name for polychoron [2] in my table.
	members.aol.com /Polycell/names.html (1343 words)

	simpex information,simplex (Site not responding. Last check: 2007-10-20)
		To be specific about the number of dimensions, sucha simpex is also called an n-simpex.
		For example, a 0-simpex is a point, a 1-simpex is a line segment, a 2-simpex is a triangle, a 3-simpex is a tetrahedron, and a 4-simpex is a pentachoron (in each case with interior).
		The convex hull of any m of the n points is also a simpex, called an m-face.
	www.vsearchmedia.com /simpex.html (404 words)

	simlex information,simplex (Site not responding. Last check: 2007-10-20)
		To be specific about the number of dimensions, sucha simlex is also called an n-simlex.
		For example, a 0-simlex is a point, a 1-simlex is a line segment, a 2-simlex is a triangle, a 3-simlex is a tetrahedron, and a 4-simlex is a pentachoron (in each case with interior).
		The convex hull of any m of the n points is also a simlex, called an m-face.
	www.vsearchmedia.com /simlex.html (404 words)

	Section 1 (Site not responding. Last check: 2007-10-20)
		Convex uniform polychora based on the pentachoron (5-cell)
		Vertices: 10 (located at the midpoints of the edges of a pentachoron, or at the centroids of its faces)
		Section 7: Uniform polychora derived from glomeric tetrahedron B
	members.aol.com /Polycell/section1.html (659 words)

	PolyGloss
		This is the gosset polytope that has a half-cube vertex-figure, and is therefore of the form 2_k1.
		For example, one can derive the pentachoron from the bipentagonal prism by numbering the vertices of one in pentagon and the other in pentagramic order.
		Likewise, the heptepeton or heptapyramid can be formed from the triheptagon prism by advancing the three bases at the rates of 1, 2 and 4.
	www.geocities.com /os2fan2/gloss.htm (16747 words)

	Science Forums and Debate - Search Results
		Cheers that helped a bunch and now I know that what I was doing was actually relevant to something.
		After a bit of searching I did find the 4-simplex referred to as a "Pentachoron" but I wasn't sure...
		I'm doing a little project at the moment to do with how triangles relate to tetrahedrons and I have some interesting results which have allowed me to calculate what the 4D version would look like.
	www.scienceforums.net /forums/search.php?do=finduser&u=2548 (625 words)

	urticator.net - The Hexadecachoron (Site not responding. Last check: 2007-10-20)
		It is a kind of pyramid with a triangular base, and has four sides that are (equilateral) triangles.
		(In case you're wondering, yes, there is also a four-dimensional analogue of the tetrahedron, namely, the pentachoron.
		It doesn't show up in the maze world.)
	www.urticator.net /maze/note-hexadeca.html (337 words)

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