cp's OEIS Frontend

A338808 Irregular table read by rows: The number of k-faced polyhedra, where k>=4, created 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.

%I A338808 #23 Dec 07 2020 01:45:19
%S A338808 8,128,56,8,0,3,450,270,82,20,10,0,2,2592,2376,972,204,168,48,0,0,5,
%T A338808 7266,7574,4550,2254,660,336,98,14,14,0,2,0,0,0,0,0,0,2,27216,31088,
%U A338808 15632,5360,1904,432,128,0,0,0,0,0,9,68778,84240,61272,33138,15714,5400,1946,720,270,126,72,18,0,0,4,0,0,0,0,0,0,0,0,4
%N A338808 Irregular table read by rows: The number of k-faced polyhedra, where k>=4, created 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 A338808 See A338806 for further details and images for this sequence.
%C A338808 The author thanks _Zach J. Shannon_ for assistance in producing the images for this sequence.
%H A338808 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 A338808 Scott R. Shannon, <a href="/A338808/a338808.jpg">4-antiprism, showing the 56 5-faced polyhedra</a>. See A338806 for an image of the full polyhedra.
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_1.jpg">4-antiprism, showing the 8 6-faced polyhedra</a>
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_2.jpg">4-antiprism, showing the 3 8-faced polyhedra</a>
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_3.jpg">7-antiprism, showing the 7266 4-faced polyhedra</a>. See A338806 for an image of the full polyhedra.
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_4.jpg">7-antiprism, showing the 7574 5-faced polyhedra</a>
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_5.jpg">7-antiprism, showing the 4550 6-faced polyhedra</a>
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_6.jpg">7-antiprism, showing the 2254 7-faced polyhedra</a>
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_7.jpg">7-antiprism, showing the 660 8-faced polyhedra</a>
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_8.jpg">7-antiprism, showing the 336 9-faced polyhedra</a>.
%H A338808 Scott R. Shannon, <a href="/A338808/a338808.png">7-antiprism, showing the 98 10-faced polyhedra</a>. None of these are visible on the surface.
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_9.jpg">7-antiprism, showing the 14 11-faced, 14 12-faced, 2 14-faced, 2 21-faced polyhedra</a>. These are colored white, black, red, yellow respectively. None of these are visible on the surface.
%H A338808 Scott R. Shannon, <a href="/A338808/a338808_1.png">10-antiprism, showing the 13 20-faced polyhedra</a>. See A338806 for an image of the full polyhedra.
%H A338808 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Antiprism.html">Antiprism</a>.
%H A338808 Wikipedia, <a href="https://en.wikipedia.org/wiki/Antiprism">Antiprism</a>.
%F A338808 Sum of row n = A338806(n).
%e A338808 The 4-antiprism is cut with 16 internal planes defined by all 3-vertex combinations of its 8 vertices. This leads to the creation of 128 4-faced polyhedra, 56 5-faced polyhedra, 8 6-faced polyhedra, and 3 8-faced polyhedra, 195 pieces in all. Note the number of 8-faced polyhedra is not a multiple of 4 - they lie directly along the z-axis so need not be a multiple of the number of edges forming the regular n-gons.
%e A338808 The table begins:
%e A338808 8;
%e A338808 128,56,8,0,3;
%e A338808 450,270,82,20,10,0,2;
%e A338808 2592,2376,972,204,168,48,0,0,5;
%e A338808 7266,7574,4550,2254,660,336,98,14,14,0,2,0,0,0,0,0,0,2;
%e A338808 27216,31088,15632,5360,1904,432,128,0,0,0,0,0,9;
%e A338808 68778,84240,61272,33138,15714,5400,1946,720,270,126,72,18,0,0,4,0,0,0,0,0,0,0,0,4;
%e A338808 194580,235880,153620,68580,25240,7460,2560,660,200,0,0,0,0,0,0,0,13;
%Y A338808 Cf. A338806 (number of polyhedra), A338801 (regular prism), A338622 (Platonic solids), A333543 (n-dimensional cube).
%K A338808 nonn,tabf
%O A338808 3,1
%A A338808 _Scott R. Shannon_, Nov 10 2020