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<p>We present the construction dynamics of the simplest pair of mutually polar nonconvex star polyhedra.The first polyhedron in this pair is Coxeter’s uniform small cubicuboctahedron, and the second is its polar-dual polyhedron, the small hexacronic icositetrahedron.We study the structure of these polyhedra and their curvatures.For the polyhedral angles of the small cubicuboctahedron, we&#xa0;obtain an analog of the Gauss–Alexandrov theorem.</p>

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Structure and Curvatures of the Small Cubicuboctahedron and Its Polar-Dual Polyhedron

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • L. A. Antipova

摘要

We present the construction dynamics of the simplest pair of mutually polar nonconvex star polyhedra.The first polyhedron in this pair is Coxeter’s uniform small cubicuboctahedron, and the second is its polar-dual polyhedron, the small hexacronic icositetrahedron.We study the structure of these polyhedra and their curvatures.For the polyhedral angles of the small cubicuboctahedron, we obtain an analog of the Gauss–Alexandrov theorem.