A363768 The values k such that a regular k-gon with all diagonals drawn contains more 3-sided cells than 4-sided cells.

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

Offset: 1

Author

Scott R. Shannon, Jun 21 2023

Keywords

• nonn

Comments

It is extremely likely that the terms in the data section form the complete list of such k-gons, although this is unknown. If more terms do exist they are greater than 875.

The only known k-gon where the number of 3-sided and 4-sided cells is equal is the 39-gon.

Examples

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

Links

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

Crossrefs

Cf. A331450, A349549, A007678.