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A128113 Number of uniform polyhedra with n edges. 6


%S 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,

%T 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,

%U 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

%N Number of uniform polyhedra with n edges.

%H Hart, George W., <a href="http://www.georgehart.com/virtual-polyhedra/uniform-info.html">Uniform Polyhedra</a>.

%H Maeder, Roman E., <a href="http://www.mathconsult.ch/showroom/unipoly/unipoly.html">Uniform Polyhedra</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UniformPolyhedron.html">Uniform Polyhedron.</a>

%F 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].

%e 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.

%Y Cf. A128112, A128114.

%K nonn

%O 1,12

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

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