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 A338806 #24 Dec 07 2020 01:45:04 %S A338806 8,195,834,6365,22770,81769,271702,688793 %N A338806 Number of polyhedra formed when an n-antiprism, formed from two n-sided regular polygons joined by 2n adjacent alternating triangles, is internally cut by all the planes defined by any three of its vertices. %C A338806 For an n-antiprism, formed from two n-sided regular polygons joined by 2n adjacent alternating triangles, create all possible internal planes defined by connecting any three of its vertices. For example, in the case of a triangular 3-antiprism this results in 3 planes. Use all the resulting planes to cut the prism into individual smaller polyhedra. The sequence lists the number of resulting polyhedra for antiprisms with n>=3. %C A338806 See A338808 for the number and images of the k-faced polyhedra in each antiprism dissection. %C A338806 The author thanks Zach J. Shannon for assistance in producing the images for this sequence. %H A338806 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 A338806 Scott R. Shannon, <a href="/A338806/a338806.png">4-antiprism, showing the 16 plane cuts on the external edges and faces</a>. %H A338806 Scott R. Shannon, <a href="/A338806/a338806_4.jpg">4-antiprism, showing the 195 polyhedra post-cutting</a>. The 4-faced polyhedra are colored red, the 5-faced polyhedra are colored orange. The 6 and 8 faced polyhedra are not visible on the surface. %H A338806 Scott R. Shannon, <a href="/A338806/a338806.jpg">4-antiprism, showing the 195 polyhedra post-cutting and exploded</a>. Each piece has been moved away from the origin by a distance proportional to the average distance of its vertices from the origin. The 6 and 8 faced polyhedra are colored yellow and green respectively. %H A338806 Scott R. Shannon, <a href="/A338806/a338806_1.png">7-antiprism, showing the 91 plane cuts on the external edges and faces</a>. %H A338806 Scott R. Shannon, <a href="/A338806/a338806_2.jpg">7-antiprism, showing the 22770 polyhedra post-cutting</a>. The 4,5,6,7,8,9 faced polyhedra are shown as red, orange, yellow, green, blue, indigo respectively. The polyhedra with 10,11,12,14,21 faces are not visible on the surface. %H A338806 Scott R. Shannon, <a href="/A338806/a338806_1.jpg">7-antiprism, showing the 22770 polyhedra post-cutting and exploded</a>. %H A338806 Scott R. Shannon, <a href="/A338806/a338806_2.png">10-antiprism, showing the 280 plane cuts on the external edges and faces</a>. %H A338806 Scott R. Shannon, <a href="/A338806/a338806_3.jpg">10-antiprism, showing the 688793 polyhedra post-cutting</a>. The 4,5,6,7,8,9,10 faced polyhedra are colored red, orange, yellow, green, blue, indigo, violet respectively. The polyhedra with 11,12,20 faces are not visible on the surface. %H A338806 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Antiprism.html">Antiprism</a>. %H A338806 Wikipedia, <a href="https://en.wikipedia.org/wiki/Antiprism">Antiprism</a>. %e A338806 a(3) = 8. The 3-antiprism is cut with 3 internal planes resulting in 8 polyhedra, all 8 pieces having 4 faces. %e A338806 a(4) = 195. The 4-antiprism is cut with 16 internal planes resulting in 195 polyhedra; 128 with 4 faces, 56 with 5 faces, 8 with 6 faces, and 3 with 8 faces. Note the number of 8-faced polyhedra is not a multiple of 4 - they lie directly along the z-axis so are not symmetric with respect to the number of edges forming the regular n-gons. %Y A338806 Cf. A338808 (number of k-faced polyhedra), A338783 (regular prism), A338571 (Platonic solids), A333539 (n-dimensional cube). %K A338806 nonn,more %O A338806 3,1 %A A338806 _Scott R. Shannon_, Nov 10 2020