

A363768


The values k such that a regular kgon with all diagonals drawn contains more 3sided cells than 4sided cells.


1



3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 32, 33, 34, 36, 38, 40, 41, 42, 43, 44, 45, 46, 48, 54, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 76, 78, 80, 82, 84, 86, 88, 94, 96, 98, 102, 108, 114, 118, 120, 126, 128, 138, 144
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OFFSET

1,1


COMMENTS

It is extremely likely that the terms in the data section form the complete list of such kgons, although this is unknown. If more terms do exist they are greater than 875.
The only known kgon where the number of 3sided and 4sided cells is equal is the 39gon.


LINKS

Scott R. Shannon, Image of the 6gon. This is the first kgon to contain both 3 and 4 sided cells and where there are more 3sided cells than 4sided cells.
Scott R. Shannon, Image of the 15gon. This is the first kgon that contains more 4sided cells than 3sided cells.
Scott R. Shannon, Image of the 39gon. This is the only known kgon that contains the same number of 3 and 4 sided cells. It is likely to be the only such kgon.


EXAMPLE

6 is a term as a regular 6gon with all diagonals drawn contains 18 3sided cells and 6 4sided cells.
144 is a term as a regular 144gon with all diagonals drawn contains 6363936 3sided cells and 6270048 4sided cells. This is likely the last such kgon.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



