A299529 Number of Johnson solids with exactly n types of faces.

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

Author

Jonathan Sondow, Feb 11 2018

Keywords

• nonn

Comments

The possible types of faces of a Johnson solid are triangles, squares, pentagons, hexagons, octagons, and decagons. See A299114 comments.

Examples

			Each of the five Johnson solids J12, J13, J17, J51, J84 has only one type of face, so a(1) = 5.
		

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.
• 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. A299114, A299530.

Formula

Sum(n>0, a(n)) = 92, the number of Johnson solids.

a(n) = 0 for n>4.