Journal of Algebraic Combinatorics

, Volume 43, Issue 3, pp 665–691 | Cite as

Classification of tight regular polyhedra

  • Gabe CunninghamEmail author
  • Daniel Pellicer


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.


Abstract regular polytope Tight polyhedron Tight polytope Flat polyhedron Flat polytope 

Mathematics Subject Classification

Primary 52B15 Secondary 51M20 05E18 52B70 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.University of Massachusetts BostonBostonUSA
  2. 2.National University of MexicoMoreliaMexico
  3. 3.Centro de Ciencias MatemáticasUniversidad Nacional Autónoma de MéxicoMoreliaMexico

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