OFFSET
1,3
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
EXAMPLE
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.
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
]
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Sep 02 2020
STATUS
approved