OFFSET
3,1
COMMENTS
See A338783 for further details and images for this sequence.
The author thanks Zach J. Shannon for assistance in producing the images for this sequence.
LINKS
Hyung Taek Ahn and Mikhail Shashkov, Geometric Algorithms for 3D Interface Reconstruction.
Scott R. Shannon, 3-prism, showing the 18 polyhedra post-cutting and exploded. 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 seventeen 4-faced polyhedra, orange the single 6-faced polyhedron.
Scott R. Shannon, 7-prism, showing the 8799 4-faced polyhedra.
Scott R. Shannon, 7-prism, showing the 10080 5-faced polyhedra.
Scott R. Shannon, 7-prism, showing the 6321 6-faced polyhedra.
Scott R. Shannon, 7-prism, showing the 3052 7-faced polyhedra.
Scott R. Shannon, 7-prism, showing the 898 8-faced polyhedra.
Scott R. Shannon, 7-prism, showing the 490 9-faced polyhedra.
Scott R. Shannon, 7-prism, showing the 161 10-faced polyhedra.
Scott R. Shannon, 7-prism, showing the 14 11-faced, 35 12-faced, 14 13-faced, 7 14-faced polyhedra. These are colored white, black, yellow, red respectively. None of these are visible on the surface.
Scott R. Shannon, 7-prism, showing all 29871 polyhedra. The 4,5,6,7,8,9,10 faced polyhedra are colored red, orange, yellow, green, blue, indigo, violet respectively. The 11,12,13,14 faced polyhedra are not visible on the surface.
Scott R. Shannon, 10-prism, showing all 594560 polyhedra.
Eric Weisstein's World of Mathematics, Prism.
Wikipedia, Prism (geometry).
FORMULA
Sum of row n = A338783(n).
EXAMPLE
The triangular 3-prism is cut with 6 internal planes defined by all 3-vertex combinations of its 6 vertices. This leads to the creation of seventeen 4-faced polyhedra and one 6-faced polyhedra, eighteen pieces in all. The single 6-faced polyhedra lies at the very center of the original 3-prism.
The 9-prism is cut with 207 internal planes leading to the creation of 319864 pieces. It is noteworthy in creating all k-faced polyhedra from k=4 to k=18.
The table begins:
17,0,1;
72,24;
575,450,232,60,15,0,3;
1728,1668,948,144,24,12;
8799,10080,6321,3052,898,490,161,14,35,14,7;
22688,24080,12784,4160,1248,272,80,32;
78327,101142,70254,39708,19584,6894,2369,1062,351,54,27,18,27,36,11;
165500,203220,134860,62520,21240,5720,1080,300,100,20;
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon, Nov 10 2020
STATUS
approved