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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..84.

Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169-200.

Eric W. Weisstein, MathWorld: 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).

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

Cf. A299114, A299530.

Sequence in context: A199584 A087675 A128044 * A014632 A117985 A115707

Adjacent sequences:  A299526 A299527 A299528 * A299530 A299531 A299532

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Feb 11 2018

STATUS

approved

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Last modified October 23 11:46 EDT 2021. Contains 348212 sequences. (Running on oeis4.)