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A299114 Number of sides of a face of an Archimedean solid. 2
3, 4, 5, 6, 8, 10 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..6.

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).


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

Sequence in context: A051954 A049821 A023729 * A103605 A098171 A039031

Adjacent sequences:  A299111 A299112 A299113 * A299115 A299116 A299117




Jonathan Sondow, Feb 02 2018



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Last modified August 5 19:49 EDT 2021. Contains 346488 sequences. (Running on oeis4.)