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Differential Geometry of Manifolds

2026 №57 (1)

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Subbotin V.I.

On non-composite RR-polytopes with conditional edges

DOI
10.5922/0321-4796-2026-57-1-7
Pages
81-92
RR polyhedron composite polyhedron with conditional edges symmetric rhombic vertex rhombic pyramid

Abstract

An RR-polyhedron is a closed convex polyhedron in E3 whose face set can be partitioned into two non-empty disjoint sets: the set of faces forming isolated faceted stars of symmetric rhombic verti­ces and the set of regular faces. If the regular faces of such a poly­hedron are of the same type, then it belongs to the first type; if they are different, then it belongs to the second type of RR-polyhedron. In the present paper, it is proved that there exist only six non-composite RR-polyhedrons of the first type with conditional edges. Two of the found RR-polyhedrons can be partitioned by planes passing through the conditional edges of the rhombic faces into regular parts, and one of the RR-polyhedrons can be partitioned in­to two rhombic pyramids.

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