A299114 -id:A299114 - cp's OEIS frontend

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

Jonathan Sondow, Feb 11 2018

nonn

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

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

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).

Cf. A299114, A299530.

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

a(n) = 0 for n>4.

A299530 Number of regular-faced convex polyhedra (excluding prisms and antiprisms) with exactly n types of faces.

Original entry on oeis.org

10, 45, 38, 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

Jonathan Sondow, Feb 11 2018

nonn

The regular-faced convex polyhedra other than prisms and antiprisms are the Platonic, Archimedean, and Johnson solids.

			Each of the five Platonic solids, and each of five Johnson solids, has one type of face, so a(1) = 5 + 5 = 10.
Each of ten Archimedean solids, and each of thirty-five Johnson solids, has two types of faces, so a(2) = 10 + 35 = 45.
Each of three Archimedean solids, and each of thirty-five Johnson solids, has three types of faces, so a(3) = 3 + 35 = 38.
Each of seventeen Johnson solids has four types of faces, so a(4) = 17.

Wikipedia, List of Johnson solids

Cf. A299114, A299529.

a(n) = 0 for n >= 5.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula