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 A338783 #29 Nov 26 2020 22:09:07 %S A338783 18,96,1335,4524,29871,65344,319864,594560 %N A338783 Number of polyhedra formed when an n-prism, formed from two n-sided regular polygons joined by n adjacent rectangles, is internally cut by all the planes defined by any three of its vertices. %C A338783 For an n-prism, formed from two n-sided regular polygons joined by n adjacent rectangles, create all possible internal planes defined by connecting any three of its vertices. For example, in the case of a triangular prism this results in 6 planes. Use all the resulting planes to cut the prism into individual smaller polyhedra. The sequence lists the number of resulting polyhedra for prisms with n>=3. %C A338783 See A338801 for the number and images of the k-faced polyhedra in each prism dissection. %C A338783 The author thanks _Zach J. Shannon_ for assistance in producing the images for this sequence. %H A338783 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 A338783 Scott R. Shannon, <a href="/A338783/a338783.png">3-prism, showing the 6 plane cuts on the external edges and faces</a>. %H A338783 Scott R. Shannon, <a href="/A338783/a338783.jpg">3-prism, showing the 18 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. Red shows the 4-faced polyhedra, orange the single 6-faced polyhedron. %H A338783 Scott R. Shannon, <a href="/A338783/a338783_2.png">7-prism, showing the 98 plane cuts on the external edges and faces</a>. %H A338783 Scott R. Shannon, <a href="/A338783/a338783_1.jpg">7-prism, showing the 29871 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 11,12,13,14 faces are not visible on the surface. %H A338783 Scott R. Shannon, <a href="/A338783/a338783_2.jpg">7-prism, showing the 29871 polyhedra post-cutting and exploded</a>. %H A338783 Scott R. Shannon, <a href="/A338783/a338783_3.png">10-prism, showing the 275 plane cuts on the external edges and faces</a> %H A338783 Scott R. Shannon, <a href="/A338783/a338783_3.jpg">10-prism, showing the 594560 polyhedra post-cutting</a>. The 4,5,6,7,8,9 faced polyhedra are colored red, orange, yellow, green, blue, indigo respectively. The polyhedra with 10,11,12,13 faces are not visible on the surface. %H A338783 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prism.html">Prism</a>. %H A338783 Wikipedia, <a href="https://en.wikipedia.org/wiki/Prism_(geometry)">Prism (geometry)</a>. %e A338783 a(3) = 18. The triangular 3-prism has 6 internal cutting planes resulting in 18 polyhedra; seventeen 4-faced polyhedra and one 6-faced polyhedron. %e A338783 a(4) = 96. The square 4-prism (a cuboid) has 14 internal cutting planes resulting in 96 polyhedra; seventy-two 4-faced polyhedra and twenty-four 5-faced polyhedra. See A338622. %Y A338783 Cf. A338801 (number of k-faced polyhedra), A338806 (antiprism), A338571 (Platonic solids), A338622 (k-faced polyhedra in Platonic solids), A333539 (n-dimensional cube). %K A338783 nonn,more %O A338783 3,1 %A A338783 _Scott R. Shannon_, Nov 08 2020