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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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497:- 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
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175:is the set {A, B, C, D}. Its convex hull is the
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382:, there are only 7 unique face arrangements.
302:shares its edge arrangement with the convex
378:For example, of the ten nonconvex regular
203:of points can be connected to form either
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192:Infinite tilings can also share common
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467:. Synonyms for special cases include
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475:for a 0-regiment (sharing vertices).
471:for a 2-regiment (sharing faces) and
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455:George Olshevsky advocates the term
405:Two (projected) polychora with same
348:A group polytopes that share both a
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298:For example, the self-intersecting
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540:(Same vertex and edge arrangement)
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487:- a set of elements of dimension
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295:while differing in their faces.
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144:can be said to have a (regular)
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491:and lower in a higher polytope.
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146:pentagonal vertex arrangement
55:Two polytopes share the same
451:Classes of similar polytopes
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342:(12 intersecting pentagons)
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442:great stellated dodecahedra
425:small stellated dodecahedra
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136:is often described by the
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522:(Same vertex arrangement)
437:Great stellated 120-cell
420:Grand stellated 120-cell
391:great stellated 120-cell
387:grand stellated 120-cell
310:Two polyhedra with same
550:Glossary for Hyperspace
532:Glossary for Hyperspace
514:Glossary for Hyperspace
380:Schläfli-Hess polychora
371:can also have the same
266:Zig-zag rhombic tiling
59:if they share the same
556:on 4 February 2007.
544:Olshevsky, George.
538:on 4 February 2007.
526:Olshevsky, George.
520:on 4 February 2007.
508:Olshevsky, George.
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205:isosceles triangles
194:vertex arrangements
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350:vertex arrangement
339:great dodecahedron
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300:great dodecahedron
291:can also share an
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201:triangular lattice
199:For example, this
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173:vertex arrangement
134:vertex arrangement
100:vertex arrangement
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74:Vertex arrangement
57:vertex arrangement
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32:vertex arrangement
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385:For example, the
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552:. Archived from
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534:. Archived from
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516:. Archived from
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407:face arrangement
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373:face arrangement
364:Face arrangement
354:edge arrangement
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284:Edge arrangement
276:Rhombille tiling
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171:(green). Its
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182:(blue). The
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369:4-polytopes
326:icosahedron
304:icosahedron
138:convex hull
528:"Regiment"
485:n-skeleton
461:n-regiment
219:with same
98:with same
61:0-skeleton
572:Polytopes
546:"Company"
289:Polyhedra
142:pentagram
125:pentagram
84:pentagram
40:polytopes
566:Category
479:See also
457:regiment
358:regiment
177:triangle
114:pentagon
96:polygons
80:pentagon
28:geometry
469:company
352:and an
257:tiling
255:rhombic
217:tilings
211:faces.
209:rhombic
166:concave
510:"Army"
48:square
36:points
440:(120
423:(120
399:cells
215:Four
164:is a
473:army
389:and
162:ABCD
94:Two
82:and
68:army
30:, a
207:or
180:ABC
26:In
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