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 A339349 #12 Dec 07 2020 01:47:47 %S A339349 2304,3000,944,408,48,24 %N A339349 The number of n-faced polyhedra formed when a cuboctahedron is internally cut by all the planes defined by any three of its vertices. %C A339349 For a cuboctahedron create all possible internal planes defined by connecting any three of its vertices. Use all the resulting planes to cut the polyhedron into individual smaller polyhedra. The sequence lists the number of resulting n-faced polyhedra, where 4 <= n <= 9. %C A339349 See A339348 for the corresponding sequence for the rhombic dodecahedron, the dual polyhedron of the cuboctahedron. %H A339349 Hyung Taek Ahn and Mikhail Shashkov, <a href="https://cnls.lanl.gov/~shashkov/papers/ahn_geometry.pdf">Geometric Algorithms for 3D Interface Reconstruction</a>. %H A339349 Scott R. Shannon, <a href="/A339349/a339349.png">Image showing the 67 internal plane cuts on the external edges and faces</a>. %H A339349 Scott R. Shannon, <a href="/A339349/a339349.jpg">Image of the 2304 4-faced polyhedra</a>. %H A339349 Scott R. Shannon, <a href="/A339349/a339349_1.jpg">Image of the 3000 5-faced polyhedra</a>. %H A339349 Scott R. Shannon, <a href="/A339349/a339349_2.jpg">Image of the 944 6-faced polyhedra</a>. %H A339349 Scott R. Shannon, <a href="/A339349/a339349_3.jpg">Image of the 408 7-faced polyhedra</a>. %H A339349 Scott R. Shannon, <a href="/A339349/a339349_4.jpg">Image of the 48 8-faced polyhedra</a>. None of these are visible on the surface of the cuboctahedron. %H A339349 Scott R. Shannon, <a href="/A339349/a339349_7.jpg">Image of the 24 9-faced polyhedra</a>. None of these are visible on the surface of the cuboctahedron. %H A339349 Scott R. Shannon, <a href="/A339349/a339349_8.jpg">Image of all 6728 polyhedra</a>. The colors are the same as those used in the above images. %H A339349 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cuboctahedron.html">Cuboctahedron</a>. %H A339349 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cuboctahedron">Cuboctahedron</a>. %e A339349 The cuboctahedron has 12 vertices, 14 faces, and 24 edges. It is cut by 67 internal planes defined by any three of its vertices, resulting in the creation of 6728 polyhedra. No polyhedra with ten or more faces are created. %Y A339349 Cf. A339348, A338622, A338801, A338808, A338825. %K A339349 nonn,fini,full %O A339349 4,1 %A A339349 _Scott R. Shannon_, Dec 01 2020