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in dimension up to 8. In dimension 3 this is due to Conway. In dimension up to 6 this is due to R. J. M. Dawson. Dimensions 7 and 8 were ruled out by R. J. M. Dawson, W. Finbow, and P.
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134:(Lángi) There are monostatic polytopes in dimension 3 with k-fold rotational symmetry for an arbitrary positive integer k.
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131:(Lángi) There are monostatic polytopes in dimension 3 whose shapes are arbitrarily close to a sphere.
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48:. The monostatic polytope in 3-space constructed independently by Guy and Knowlton has 19
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A polytope is called monostatic if, when filled homogeneously, it is stable on only one
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128:(R. J. M. Dawson) There exist monostatic simplices in dimension 10 and up.
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Z. Lángi, A solution to some problems of Conway and Guy on monostable polyhedra,
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Wolfram
Demonstrations Project: Bezdek's Unistable Polyhedron With 18 Faces
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R. J. M. Dawson, W. Finbow, P. Mak, Monostatic simplexes. II.
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which "can stand on only one face". They were described in 1969 by
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R. J. M. Dawson, W. Finbow, Monostatic simplexes. III.
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International
Journal of Computational Geometry & Applications
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H. Croft, K. Falconer, and R. K. Guy, Problem B12 in
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293:A. Reshetov, A unistable polyhedron with 14 faces.
253:R. J. M. Dawson, Monostatic simplexes.
61:3D model of R. K. Guy's monostatic polyhedron
84:. Alternatively, a polytope is monostatic if its
109:in the plane is monostatic. This was shown by
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239:, A unistable polyhedron with only 19 faces,
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287:Lectures on Discrete and Polyhedral Geometry
71:3D model of Reshetov's monostatic polyhedron
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250:, New York: Springer-Verlag, p. 61, 1991.
241:Bell Telephone Laboratories MM 69-1371-3
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195:"A unistable polyhedron with 14 faces"
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193:Reshetov, Alexander (May 13, 2014),
96:in the interior of only one facet.
328:YouTube: The uni-stable polyhedron
257:92 (1985), no. 8, 541–546.
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278:54 (2022), no. 2, 501–516.
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248:Unsolved Problems in Geometry
358:. You can help Knowledge by
295:Int. J. Comput. Geom. Appl.
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271:84 (2001), 101–113.
264:70 (1998), 209–219.
211:10.1142/S0218195914500022
171:"Stability of polyhedra"
120:There are no monostatic
297:24 (2014), 39–60.
354:-related article is a
314:"Unistable polyhedron"
276:Bull. Lond. Math. Soc.
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113:via reduction to the
94:orthogonal projection
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233:(1969), 78–82.
26:unistable polyhedron
255:Amer. Math. Monthly
237:K. C. Knowlton
115:four-vertex theorem
46:K. C. Knowlton
22:monostatic polytope
311:Weisstein, Eric W.
225:, M. Goldberg and
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229:, Problem 66-12,
223:J. H. Conway
38:J. H. Conway
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177:. Retrieved
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399:Categories
352:polyhedron
179:2018-07-09
156:References
100:Properties
76:Definition
410:Polyhedra
319:MathWorld
122:simplices
111:V. Arnold
92:) has an
282:Igor Pak
139:See also
86:centroid
34:polytope
18:geometry
28:) is a
145:Gömböc
350:This
174:(PDF)
88:(the
82:facet
50:faces
356:stub
125:Mak.
44:and
24:(or
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105:No
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