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

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

1,1

Comments

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

Links

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

Wikipedia, List of Johnson solids

Formula

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

Example

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.

Crossrefs

Cf. A299114, A299529.

Sequence in context: A240383 A160970 A202296 * A238982 A292611 A275623

Adjacent sequences: A299527 A299528 A299529 * A299531 A299532 A299533

Keyword

nonn

Author

Jonathan Sondow, Feb 11 2018

Status

approved