A128113 Number of uniform polyhedra with n edges.

0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 3, 0, 0, 2, 1, 0, 2, 0, 3, 3, 0, 0, 6, 0, 0, 3, 4, 0, 8, 0, 3, 5, 0, 0, 9, 0, 0, 6, 2, 0, 3, 0, 7, 4, 0, 0, 13, 0, 0, 8, 8, 0, 3, 0, 4, 9, 0, 0, 22, 0, 0, 6, 5, 0, 5, 0, 11, 11, 0, 0, 11, 0, 0, 10, 12, 0, 6, 0, 6, 9, 0, 0, 14, 0, 0, 14, 6, 0, 10, 0, 15, 15, 0, 0, 13, 0, 0

Offset

1,12

Links

Table of n, a(n) for n=1..98.

Hart, George W., Uniform Polyhedra.

Maeder, Roman E., Uniform Polyhedra.

Eric Weisstein's World of Mathematics, Uniform Polyhedron.

Formula

After 240th term, a(n) equals the sum between [A055684(n/3) + 1 for n != 0 mod 3, otherwise 0] and [A055684(n/4) + A128115(n/4) + 1 for n != 0 mod 4, otherwise 0].

Example

The first nonzero term, a(6)=1, represents the polyhedron with least edges: the tetrahedron. There is no polyhedron with 7 edges and no polyhedron with 8 edges is uniform, a(9)=1 represents the triangular prism, the next nonzero term, a(12), is 3 because there are the tetrahemihexahedron, the cube and the octahedron.

Crossrefs

Cf. A128112, A128114.

Sequence in context: A067168 A099475 A120569 * A108930 A059682 A357317

Adjacent sequences: A128110 A128111 A128112 * A128114 A128115 A128116

Keyword

nonn

Author

Paulo de A. Sachs (sachs6(AT)yahoo.de), Feb 15 2007, corrected Feb 15 2007

Status

approved