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of the convex hull is the set {A, B, C}, which is not the same as that of the quadrilateral; so here, the convex hull is not a way to describe the vertex arrangement.
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508:- A local arrangement of faces in a polyhedron (or arrangement of cells in a polychoron) around a single vertex.
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which means they have similar vertex, edge, and face arrangements, but may differ in their cells.
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is understood to mean four points in a plane, equal distance and angles from a center point.
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The same set of vertices can be connected by edges in different ways. For example, the
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in space described by their relative positions. They can be described by their use in
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For the local description of faces around a vertex of a polyhedron or tiling, see
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faces, appear visually indistinguishable without a representation of their
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for a set of polytopes that share an edge arrangement, and more generally
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A group of polytopes that shares a vertex arrangement is called an
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for a set of polytopes that share elements up to dimension
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polytope which contains it. For example, the regular
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Set of points described by relative position in space
186:is the set {A, B, C, D}. Its convex hull is the
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393:, there are only 7 unique face arrangements.
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313:shares its edge arrangement with the convex
389:For example, of the ten nonconvex regular
214:of points can be connected to form either
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203:Infinite tilings can also share common
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466:George Olshevsky advocates the term
416:Two (projected) polychora with same
359:A group polytopes that share both a
309:For example, the self-intersecting
551:(Same vertex and edge arrangement)
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498:- a set of elements of dimension
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306:while differing in their faces.
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155:can be said to have a (regular)
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502:and lower in a higher polytope.
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157:pentagonal vertex arrangement
66:Two polytopes share the same
462:Classes of similar polytopes
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353:(12 intersecting pentagons)
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453:great stellated dodecahedra
436:small stellated dodecahedra
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147:is often described by the
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533:(Same vertex arrangement)
448:Great stellated 120-cell
431:Grand stellated 120-cell
402:great stellated 120-cell
398:grand stellated 120-cell
321:Two polyhedra with same
561:Glossary for Hyperspace
543:Glossary for Hyperspace
525:Glossary for Hyperspace
391:Schläfli-Hess polychora
382:can also have the same
277:Zig-zag rhombic tiling
70:if they share the same
567:on 4 February 2007.
555:Olshevsky, George.
549:on 4 February 2007.
537:Olshevsky, George.
531:on 4 February 2007.
519:Olshevsky, George.
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216:isosceles triangles
205:vertex arrangements
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361:vertex arrangement
350:great dodecahedron
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311:great dodecahedron
302:can also share an
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212:triangular lattice
210:For example, this
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184:vertex arrangement
145:vertex arrangement
111:vertex arrangement
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99:vertex arrangement
85:Vertex arrangement
68:vertex arrangement
61:vertex arrangement
43:vertex arrangement
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396:For example, the
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255:Triangular tiling
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16:(Redirected from
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563:. Archived from
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545:. Archived from
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527:. Archived from
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418:face arrangement
384:face arrangement
375:Face arrangement
365:edge arrangement
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304:edge arrangement
295:Edge arrangement
287:Rhombille tiling
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245:Lattice points
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513:External links
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506:Vertex figure
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182:(green). Its
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565:the original
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193:(blue). The
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380:4-polytopes
337:icosahedron
315:icosahedron
149:convex hull
539:"Regiment"
496:n-skeleton
472:n-regiment
230:with same
109:with same
72:0-skeleton
583:Polytopes
557:"Company"
300:Polyhedra
153:pentagram
136:pentagram
95:pentagram
51:polytopes
577:Category
490:See also
468:regiment
369:regiment
188:triangle
125:pentagon
107:polygons
91:pentagon
39:geometry
480:company
363:and an
268:tiling
266:rhombic
228:tilings
222:faces.
220:rhombic
177:concave
521:"Army"
59:square
47:points
451:(120
434:(120
410:cells
226:Four
175:is a
484:army
400:and
173:ABCD
105:Two
93:and
79:army
41:, a
218:or
191:ABC
37:In
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