期刊
ARS MATHEMATICA CONTEMPORANEA
卷 19, 期 1, 页码 95-124出版社
UP FAMNIT
DOI: 10.26493/1855-3974.2120.085
关键词
Polyhedron; static equilibrium; monostatic polyhedron; f-vector
资金
- BMEWater Sciences & Disaster Prevention TKP2020 IE grant of NKFIH Hungary (BME IE-VIZ TKP2020)
- NKFIH grant [K119245]
We define the mechanical complexity C(P) of a 3-dimensional convex polyhedron P, interpreted as a homogeneous solid, as the difference between the total number of its faces, edges and vertices and of its static equilibria; and the mechanical complexity C(S, U) of primary equilibrium classes (S, U)(E) with S stable and U unstable equilibria as the infimum of the mechanical complexity of all polyhedra in that class. We prove that the mechanical complexity of a class (S, U)(E) with S, U > 1 is the minimum of 2(f + v S - U) over all polyhedral pairs (f, v), where a pair of integers is called a polyhedral pair if there is a convex polyhedron with f faces and v vertices. In particular, we prove that the mechanical complexity of a class (S, U)(E) is zero if and only if there exists a convex polyhedron with S faces and U vertices. We also give asymptotically sharp bounds for the mechanical complexity of the monostatic classes (1, U)(E) and (S, 1)(E), and offer a complexity-dependent prize for the complexity of the Gomboc-class (1, 1)(E).
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据