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A299114
Number of sides of a face of an Archimedean solid.
2
3, 4, 5, 6, 8, 10
OFFSET
1,1
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
Victor A. Zalgaller, Convex Polyhedra with Regular Faces, Zap. Nauchn. Sem. LOMI, 1967, Volume 2. Pages 5-221 (Mi znsl1408).
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Jonathan Sondow, Feb 02 2018
STATUS
approved