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or edge-skeleton, a graph whose vertices are the geometric vertices of the polyhedron and whose edges correspond to the geometric edges. Conversely, the graphs that are skeletons of three-dimensional polyhedra can be characterized by
311:-dimensional convex polytope. Similarly, in a polyhedron, exactly two two-dimensional faces meet at every edge, while in higher dimensional polytopes three or more two-dimensional faces meet at every edge.
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365: − 3)-dimensional feature. Thus, the edges of a polygon are its facets, the edges of a 3-dimensional
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Proceedings of the
Eighteenth Annual ACM Symposium on Theory of Computing (STOC '86)
499:(2000), "Bridges between geometry and graph theory", in Gorini, Catherine A. (ed.),
153:. In a polyhedron or more generally a polytope, an edge is a line segment where two
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Shaping Space: Exploring
Polyhedra in Nature, Art, and the Geometrical Imagination
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Line segment joining two adjacent vertices in a polygon or polytope
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107:Every edge is shared by three or more faces in a
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512:. See in particular Theorem 3,
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539:Pacific Journal of Mathematics
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279:. This equation is known as
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692:Multi-dimensional geometry
452:". From Wolfram MathWorld.
439:". From Wolfram MathWorld.
281:Euler's polyhedron formula
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249:{\displaystyle V-E+F=2,}
145:, or higher-dimensional
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315:Alternative terminology
371:4-dimensional polytope
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408:Lectures on Polytopes
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211:Euler characteristic
687:Elementary geometry
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32:Edge (graph theory)
660:Weisstein, Eric W.
641:Weisstein, Eric W.
463:Senechal, Marjorie
403:Ziegler, Günter M.
301:Balinski's theorem
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192:3-vertex-connected
188:Steinitz's theorem
663:"Polyhedral edge"
577:Polyhedron Models
367:convex polyhedron
275:is the number of
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514:p. 176
303:, at least
681:Categories
389:References
143:polyhedron
109:4-polytope
89:polyhedron
697:Polytopes
668:MathWorld
649:MathWorld
226:−
113:tesseract
529:(1961),
465:(2013),
405:(1995),
377:See also
339:polytope
265:vertices
183:skeleton
159:diagonal
147:polytope
135:vertices
123:geometry
53:triangle
49:vertices
622:8342016
561:0126765
535:-space"
509:1782654
139:polygon
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361:is a (
351:is a (
297:vertex
259:where
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618:S2CID
348:ridge
333:of a
326:facet
277:faces
173:, an
155:faces
137:in a
125:, an
87:in a
85:faces
51:of a
582:ISBN
473:ISBN
417:ISBN
358:peak
331:side
323:, a
285:cube
205:Any
175:edge
127:edge
93:cube
610:doi
547:doi
329:or
169:In
121:In
683::
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616:,
557:MR
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363:d
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273:F
269:E
261:V
244:,
241:2
238:=
235:F
232:+
229:E
223:V
115:.
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34:.
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
