Geodesic
On the existence and completeness of enumeration of three-dimensional $RR$-polyhedra
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 106-115.

Voir la notice de l'article provenant de la source Math-Net.Ru

An $RR$-polyhedron is a closed convex polyhedron in $E^3$ whose set of faces can be divided into two nonempty disjoint class: the class of regular polygons of the same type and the class of faces that form stars of symmetric rhombic vertices. A theorem on the existence and completeness of enumeration of closed convex three-dimensional $RR$-polyhedra is proved.
Keywords: $RR$-polyhedron, star of a vertex, symmetric rhombic vertex. 
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V. I. Subbotin. On the existence and completeness of enumeration of three-dimensional $RR$-polyhedra. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 106-115. http://geodesic.mathdoc.fr/item/INTO_2022_216_a10/

[1] Deza M., Grishukhin V. P., Shtogrin A. I., Izometricheskie poliedralnye podgrafy v giperkubakh i kubicheskikh reshetkakh, MTsNMO, M., 2007

[2] Zalgaller V. A., “Vypuklye mnogogranniki s pravilnymi granyami”, Zap. nauch. semin. LOMI., 2 (1967), 1–220

[3] Emelichev V. A., Kovalev M. M., Kravtsov M. K., Mnogogranniki. Grafy. Optimizatsiya, Nauka, M., 1981 | MR

[4] Subbotin V. I., “O dvukh klassakh mnogogrannikov s rombicheskimi vershinami”, Zap. nauch. semin. POMI., 476 (2018)

[5] Subbotin V. I., “O polnote spiska vypuklykh $RR$-mnogogrannikov”, Chebyshev. sb., 1 (2020), 297–309

[6] Coxeter H. S. M., “Regular and semi-regular polytopes, III”, Math. Z., 200:21 (1988), 3–45 | DOI | MR

[7] Cromwell P. R., Polyhedra, Cambridge Univ. Press, Cambridge, 1999 | MR

[8] Grunbaum B., “Regular polyhedra—old and new”, Aequat. Math., 16 (1977), 1–20 | DOI | MR

[9] Grunbaum B., “New uniform polyhedra”, Discrete Geometry: In Honor of W. Kuperberg's 60th Birthday, ed. Bezdek A., Marcel Dekker, New York, 2003, 331–350 | DOI | MR

[10] Johnson N. W., “Convex polyhedra with regular faces”, Can. J. Math., 18:1 (1966), 169–200 | DOI | MR