This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A180916 #34 Feb 16 2025 08:33:13
%S A180916 0,0,0,1,2,3,2,7,3,6,4,7,3,13,2,5,4,6,1,9,2,6,1,4,1,8,4,2,1,3,1,10,1,
%T A180916 3,1,2,4,3,1,2,1,9,1,2,1,2,2,2,1,2,1,9,1,2,1,2,1,2,1,2,1,9,1,2,1,2,1,
%U A180916 2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,3,1,2,1,2,1,2,1,2
%N A180916 Number of convex polyhedra with n faces that are all regular polygons.
%C A180916 For all n > 92, the sequence is identical to A000034 because for large n only prisms (even and odd n) and antiprisms (even n) are convex and have regular polygonal faces. The MathWorld article about Johnson Solids is very informative about this topic.
%C A180916 In a regular-faced polyhedron, any two faces with the same number of edges are congruent. (Proof: As the two faces are regular polygons, it suffices to show their edges have the same length. But as all faces are regular polygons and the polyhedron is connected, all edges have the same length.) - _Jonathan Sondow_, Feb 11 2018
%H A180916 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/Cube.html">MathWorld: Cube</a>
%H A180916 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PentagonalPyramid.html">MathWorld: Pentagonal Pyramid</a>
%H A180916 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/Dipyramid.html">MathWorld: Dipyramid</a>
%H A180916 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PentagonalPrism.html">MathWorld: Pentagonal Prism</a>
%H A180916 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/ElongatedTriangularPyramid.html">MathWorld: Elongated Triangular Pyramid</a>
%H A180916 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/HexagonalPyramid.html">MathWorld: Hexagonal Pyramid</a>
%H A180916 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/JohnsonSolid.html">MathWorld: Johnson Solid </a>
%F A180916 a(A296602(n)) = 1. - _Jonathan Sondow_, Jan 29 2018
%e A180916 a(6) = 3 because the cube, pentagonal pyramid, and triangular bipyramid all qualify. a(7) = 2 because only the pentagonal prism and elongated triangular pyramid qualify; the hexagonal pyramid is impossible with equilateral triangles
%t A180916 f = Tally[Join[PolyhedronData["Platonic", "FaceCount"], PolyhedronData["Archimedean", "FaceCount"], PolyhedronData["Johnson", "FaceCount"], {PolyhedronData[{"Prism", 3}, "FaceCount"]}]]; f2 = Transpose[f]; cnt = Table[0, {n, 100}]; cnt[[f2[[1]]]] = f2[[2]]; Do[cnt[[n]]++, {n, 7, 100}] (* add prisms *); Do[ cnt[[n]]++, {n, 10, 100, 2}] (* add antiprisms *); cnt (* _T. D. Noe_, Mar 04 2011 *)
%Y A180916 Cf. A296602, A296603, A296604.
%K A180916 nice,nonn
%O A180916 1,5
%A A180916 _J. Lowell_, Sep 23 2010
%E A180916 More terms from _J. Lowell_, Feb 28 2011
%E A180916 Corrected by _T. D. Noe_, Mar 04 2011