Geodesic
Classification of tight regular polyhedra
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 3, pp. 665-691.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

A regular polyhedron of type $\{p, q\}$ has at least 2pq flags, and it is called tight if it has exactly 2pq flags. The values of $p$ and $q$ for which there exist tight orientably regular polyhedra were previously known. We determine for which values of $p$ and $q$ there is a tight non-orientably regular polyhedron of type $\{p, q\}$. Furthermore, we completely classify tight regular polyhedra in terms of their automorphism groups.
Classification : 52B15, 51M20, 05E18, 52B70
Keywords: abstract regular polytope, tight polyhedron, tight polytope, flat polyhedron, flat polytope 
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     title = {Classification of tight regular polyhedra},
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     language = {en},
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Cunningham, Gabe; Pellicer, Daniel. Classification of tight regular polyhedra. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 3, pp. 665-691. http://geodesic.mathdoc.fr/item/JAC_2016__43_3_a3/