A299114 Number of sides of a face of an Archimedean solid.

3, 4, 5, 6, 8, 10

Offset: 1

Author

Jonathan Sondow, Feb 02 2018

Keywords

• nonn
• fini
• full

Comments

Values of n for which the regular n-gon is a face of some Archimedean solid.

Remarkably, the same is true for Johnson solids. Indeed, before Johnson (1966) and Zalgaller (1967) classified the 92 Johnson solids, Grünbaum and Johnson (1965) proved that the only polygons that occur as faces of a non-uniform regular-faced convex polyhedron (i.e., a Johnson solid) are triangles, squares, pentagons, hexagons, octagons, and decagons.

Links

• Branko Grünbaum, Norman Johnson, The faces of a regular-faced polyhedron, J. Lond. Math. Soc. 40, 577-586 (1965).
• Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169-200.
• Joseph Malkevitch, Regular-Faced Polyhedra: Remembering Norman Johnson, AMS Feature Column, Jan. 2018.
• Eric Weisstein's World of Mathematics, Archimedean Solid
• Wikipedia, List of Johnson solids
• Victor A. Zalgaller, Convex Polyhedra with Regular Faces, Zap. Nauchn. Sem. LOMI, 1967, Volume 2. Pages 5-221 (Mi znsl1408).

Crossrefs

Cf. A092536, A092537, A092538, A242731, A242732, A242733.