A333657 a(n) is the number of convex polyhedra whose faces are regular polygons and whose largest face is an n-gon.

0, 0, 8, 30, 37, 14, 2, 9, 2, 22, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Peter Kagey, Sep 02 2020

Keywords

• nonn

Examples

			For n = 3, the a(3) = 8 polyhedra consisting of only equilateral triangles are: the tetrahedron, the octahedron, the icosahedron, and the Johnson solids J_12, J_13, J_17, J_51, and J_84.
For n = 8, the a(8) = 9 polyhedra containing an octagonal face but no face with more than eight sides are: the truncated cube, the truncated cuboctahedron, the octagonal prism, the octagonal antiprism, and the Johnson solids J_4, J_19, J_23, J_66, and J_67.
For n > 10, the a(n) = 2 polyhedra are the n-gonal prism and the n-gonal antiprism.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..1000
• Mathematics Stack Exchange, Number of convex polyhedra whose faces are regular polygons and whose largest face is an n-gon

Crossrefs

Cf. A180916, A299529.

Programs

Mathematica

MaxFace[l_] := Max[Length /@ l];
a[n_] := Count[
  Join[
    MaxFace /@ PolyhedronData["Platonic", "FaceIndices"],
    MaxFace /@ PolyhedronData["Archimedean", "FaceIndices"],
    MaxFace /@ PolyhedronData["Johnson", "FaceIndices"],
    Range[4, n], (*Prisms, including triangular prism, excluding cube*)
    Range[4, n]  (*Antiprisms, excluding octahedron*)
  ],
  n
]