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In geometry, a monostatic polytope (or unistable polyhedron) is a ''d''-polytope which "can stand on only one face". They were described in 1969 by J.H. Conway, M. Goldberg and R.K. Guy. The monostatic polytope in 3-space they constructed has 19 faces. In 2012, Andras Bezdek has discovered a 18 face solution and, in 2014, Alex Reshetov has published a 14 face object. == Definition == A polytope is called monostatic if, when filled homogeneously, it is stable on only one facet. Alternatively, a polytope is monostatic if its centroid (the center of mass) has an orthogonal projection in the interior of only one facet. == Properties == * No convex polygon in the plane is monostatic. This was shown by V. Arnold via reduction to the four-vertex theorem. * There are no monostatic simplices 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. Mak. * (R.J.M. Dawson) There exist monostatic simplices in dimension 10 and up. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Monostatic polytope」の詳細全文を読む スポンサード リンク
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