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 A339348 #13 Dec 07 2020 01:47:35 %S A339348 8976,8976,3936,1440,672 %N A339348 The number of n-faced polyhedra formed when a rhombic dodecahedron is internally cut by all the planes defined by any three of its vertices. %C A339348 For a rhombic dodecahedron 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 <= 8. %C A339348 See A339349 for the corresponding sequence for the cubooctahedron, the dual polyhedron of the rhombic dodecahedron. %H A339348 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 A339348 Scott R. Shannon, <a href="/A339348/a339348.png">Image showing the 103 internal plane cuts on the external edges and faces</a>. %H A339348 Scott R. Shannon, <a href="/A339348/a339348.jpg">Image of the 8976 4-faced polyhedra</a>. %H A339348 Scott R. Shannon, <a href="/A339348/a339348_1.jpg">Image of the 8976 5-faced polyhedra</a>. %H A339348 Scott R. Shannon, <a href="/A339348/a339348_2.jpg">Image of the 3936 6-faced polyhedra</a>. %H A339348 Scott R. Shannon, <a href="/A339348/a339348_3.jpg">Image of the 1440 7-faced polyhedra</a>. %H A339348 Scott R. Shannon, <a href="/A339348/a339348_4.jpg">Image of the 672 8-faced polyhedra</a>. %H A339348 Scott R. Shannon, <a href="/A339348/a339348_5.jpg">Image of the 672 8-faced polyhedra from directly above a vertex</a>. %H A339348 Scott R. Shannon, <a href="/A339348/a339348_6.jpg">Image of all 24000 polyhedra</a>. The colors are the same as those used in the above images. %H A339348 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RhombicDodecahedron.html">Rhombic Dodecahedron</a>. %H A339348 Wikipedia, <a href="https://en.wikipedia.org/wiki/Rhombic_dodecahedron">Rhombic dodecahedron</a>. %e A339348 The rhombic dodecahedron has 14 vertices, 12 faces, and 24 edges. It is cut by 103 internal planes defined by any three of its vertices, resulting in the creation of 24000 polyhedra. No polyhedra with nine or more faces are created. %Y A339348 Cf. A339349, A338622, A338801, A338808, A338825. %K A339348 nonn,fini,full %O A339348 4,1 %A A339348 _Scott R. Shannon_, Dec 01 2020