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A333657
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a(n) is the number of convex polyhedra whose faces are regular polygons and whose largest face is an n-gon.
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3
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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
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OFFSET
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1,3
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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
]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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