On free angles of 𝑅𝑅-polyhedra
https://doi.org/10.22405/2226-8383-2026-27-1-97-110
Abstract
This article derives formulas for free angles of various orders of RR-polytopes and applies the resulting relations to prove the completeness of the list of non-composite RR-polytopes of the second type with acute-angled rhombic vertices. Free angles of the first order are flat angles whose vertices belong to the rhombic stars of the RR-polytopes. The sides of each free angle of the first order are two sides of adjacent rhombi of the rhombic star. Previously, the author found a relationship between the acute angles of the rhombic vertex rhombi and free angles of the first order. Here, we will establish relationships between the flat angles between two sides of regular polygons glued into free angles of the first order and the acute angles of the rhombi.
The angles between the sides of regular faces are called free angles of the second order in this article. Similarly, the sides of adjacent regular polygons glued into free angles of the second order form an angle called a free angle of the third order. All possible cases of gluing one or two identical regular polygons into free angles are considered, which makes it possible to establish the completeness of the list of non-composite 𝑅𝑅-polyhedra with acute-angled rhombic vertices and regular faces of various types.
About the Author
Vladimir Ivanovich Subbotin
Platov South Russian State polytechnic university (NPI); Don State Agrarian University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
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For citations:
Subbotin V.I. On free angles of 𝑅𝑅-polyhedra. Chebyshevskii Sbornik. 2026;27(1):97-110. (In Russ.) https://doi.org/10.22405/2226-8383-2026-27-1-97-110
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