OFFSET
3,9
COMMENTS
See A351045 for details of an edge's count of facing edges in an n-gon with all diagonals drawn.
For n = 3 to n = 80 the regions with edges all with a different number of facing edges are all triangles or quadrilaterals. The 81-gon is the first n-gon to contain pentagons with this property. The largest number of edges possible for such regions is unknown.
LINKS
Scott R. Shannon, Table of n, a(n) for n = 3..140
Scott R. Shannon, Image for n = 11. This is the first n-gon to contain regions whose edges all have a different facing edge count. In this and other images such regions are highlighted in gray.
Scott R. Shannon, Image for n = 13.
Scott R. Shannon, Image for n = 18.
Scott R. Shannon, Image for n = 81. This is zoomed-in on one of the pentagons whose edges all have a different facing edge count: 6,7,8,9,10.
EXAMPLE
a(11) = 44. The 11-gon contains forty-four triangles whose three edges all have a different number of facing edges. This is the first n-gon to contain such regions. See the attached image.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon and N. J. A. Sloane, Feb 03 2022
STATUS
approved