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A299529
Number of Johnson solids with exactly n types of faces.
4
5, 35, 35, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
1,1
COMMENTS
The possible types of faces of a Johnson solid are triangles, squares, pentagons, hexagons, octagons, and decagons. See A299114 comments.
LINKS
Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169-200.
Eric Weisstein's World of Mathematics, Johnson Solid.
Victor A. Zalgaller, Convex Polyhedra with Regular Faces, Zap. Nauchn. Sem. LOMI, 1967, Volume 2. Pages 5-221 (Mi znsl1408).
FORMULA
Sum(n>0, a(n)) = 92, the number of Johnson solids.
a(n) = 0 for n>4.
EXAMPLE
Each of the five Johnson solids J12, J13, J17, J51, J84 has only one type of face, so a(1) = 5.
CROSSREFS
Sequence in context: A087675 A376610 A128044 * A014632 A117985 A371561
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Feb 11 2018
STATUS
approved