A128114 -id:A128114 - cp's OEIS frontend

A128112 Number of uniform polyhedra with n faces.

0, 0, 0, 1, 1, 1, 3, 3, 3, 4, 3, 10, 5, 7, 6, 7, 4, 11, 8, 12, 9, 8, 6, 16, 11, 13, 10, 14, 9, 10, 14, 19, 15, 13, 10, 19, 12, 11, 18, 21, 12, 16, 20, 20, 21, 16, 12, 26, 23, 14, 21, 25, 16, 22, 26, 21, 20, 20, 18, 33, 29, 18, 30, 35, 18, 27, 24, 23, 33, 26, 22, 28, 35, 20, 36, 42

Offset: 1

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

nonn

			a(20)=12 because there are the icosahedron, the small cubicuboctahedron, the great cubicuboctahedron, the cubitruncated cuboctahedron, the great icosahedron, the octadecagonal prism, two octadecagrammic (18/5 and 18/7) prisms, the enneagonal antiprism, two enneagrammic (9/2 and 9/4) antiprisms and the enneagrammic crossed antiprism.

Hart, George W., Uniform Polyhedra.
Maeder, Roman E., Uniform Polyhedra.
Eric Weisstein's World of Mathematics, Uniform Polyhedron.

Cf. A128113, A128114.

After 124th term, a(n) equals A055684(n-2) + 1 for n odd and A055684(n-2) + A055684(n/2-1) + A128115(n/2-1) + 2 for n even.

A128113 Number of uniform polyhedra with n edges.

Original entry on oeis.org

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

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

nonn

			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.

Hart, George W., Uniform Polyhedra.
Maeder, Roman E., Uniform Polyhedra.
Eric Weisstein's World of Mathematics, Uniform Polyhedron.

Cf. A128112, A128114.

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].

A128914 Number of uniform polyhedra with 2n vertices.

Original entry on oeis.org

0, 1, 3, 2, 5, 10, 7, 5, 7, 9, 12, 15, 14, 7, 18, 9, 19, 7, 21, 10, 14, 11, 26, 12, 23, 14, 21, 14, 33, 42, 35, 19, 23, 18, 28, 14, 42, 21, 28, 18, 47, 14, 49, 24

Offset: 1