论文标题
凸锥由常规多面体跨越
Convex cones spanned by regular polytopes
论文作者
论文摘要
我们研究了三个多面体锥的家族，它们的切片是普通的简单，立方体和交叉聚焦的。我们计算这些锥体的固体角度和圆锥固有体积。我们表明，在随机几何形状中出现的几个量可以通过这些圆锥固有体积来表达。 A list of such quantities includes internal and external solid angles of regular simplices and crosspolytopes, the probability that a (symmetric) Gaussian random polytope or the Gaussian zonotope contains a given point, the expected number of faces of the intersection of a regular polytope with a random linear subspace passing through its centre, and the expected number of faces of the projection of a regular polytope onto a random linear subspace.
We study three families of polyhedral cones whose sections are regular simplices, cubes, and crosspolytopes. We compute solid angles and conic intrinsic volumes of these cones. We show that several quantities appearing in stochastic geometry can be expressed through these conic intrinsic volumes. A list of such quantities includes internal and external solid angles of regular simplices and crosspolytopes, the probability that a (symmetric) Gaussian random polytope or the Gaussian zonotope contains a given point, the expected number of faces of the intersection of a regular polytope with a random linear subspace passing through its centre, and the expected number of faces of the projection of a regular polytope onto a random linear subspace.
