

A299114


Number of sides of a face of an Archimedean solid.


2




OFFSET

1,1


COMMENTS

Values of n for which the regular ngon 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 nonuniform regularfaced convex polyhedron (i.e., a Johnson solid) are triangles, squares, pentagons, hexagons, octagons, and decagons.


LINKS

Table of n, a(n) for n=1..6.
Branko Grünbaum, Norman Johnson, The faces of a regularfaced polyhedron, J. Lond. Math. Soc. 40, 577586 (1965).
Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169200.
Joseph Malkevitch, RegularFaced 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 5221 (Mi znsl1408).


CROSSREFS

Cf. A092536, A092537, A092538, A242731, A242732, A242733.
Sequence in context: A051954 A049821 A023729 * A103605 A098171 A039031
Adjacent sequences: A299111 A299112 A299113 * A299115 A299116 A299117


KEYWORD

nonn,fini,full


AUTHOR

Jonathan Sondow, Feb 02 2018


STATUS

approved



