A359201 Number of edges of regular m-polytopes for m >= 3.

6, 10, 12, 15, 21, 24, 28, 30, 32, 36, 40, 45, 55, 60, 66, 78, 80, 84, 91, 96, 105, 112, 120, 136, 144, 153, 171, 180, 190, 192, 210, 220, 231, 253, 264, 276, 300, 312, 325, 351, 364, 378, 406, 420, 435, 448, 465, 480, 496, 528, 544, 561, 595, 612, 630, 666

Offset: 1

Author

Marco Ripà, Dec 20 2022

Keywords

• easy
• nonn

Comments

In 3 dimensions there are five (convex) regular polytopes and they have 6, 12, or 30 edges (A063722).

In 4 dimensions there are six regular 4-polytopes and they have 10, 24, 32, 96, 720, or 1200 edges (A063926).

In m >= 5 dimensions, there are only 3 regular polytopes (i.e., the m-simplex, the m-cube, and the m-crosspolytope) so that we can sort their number of edges in ascending order and define the present sequence.

Examples

			6 is a term since a tetrahedron has 6 edges.
		

Links

• Mathematics StackExchange, What are the formulas for the number of vertices, edges, faces, cells, 4-faces, ..., n-faces, of convex regular polytopes in n≥5 dimensions?
• Wikipedia, List of regular polytopes and compounds

Crossrefs

Cf. A000217, A001787, A046092, A063722, A063926.

Cf. A359202 (faces), A359662 (cells).

Formula

{a(n), n >= 1} = {{30, 96, 720} U {A000217} U {A001787} U {A046092}} \ {0, 1, 3, 4}.