A359202 Number of (bidimensional) faces of regular m-polytopes for m >= 3.

4, 6, 8, 10, 12, 20, 24, 32, 35, 56, 80, 84, 96, 120, 160, 165, 220, 240, 280, 286, 364, 448, 455, 560, 672, 680, 720, 816, 960, 969, 1140, 1200, 1320, 1330, 1540, 1760, 1771, 1792, 2024, 2288, 2300, 2600, 2912, 2925, 3276, 3640, 3654, 4060, 4480, 4495, 4608

Offset: 1

Author

Marco Ripà, Dec 20 2022

Keywords

• easy
• nonn

Comments

In 3 dimensions there are five (convex) regular polytopes and they have 4, 6, 8, 12, or 20 (bidimensional) faces (A053016).

In 4 dimensions there are six regular 4-polytopes and they have 10, 24, 32, 96, 720, or 1200 faces (A063925).

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 bidimensional faces in ascending order and define the present sequence.

Examples

			6 is a term since a cube has 6 faces.
		

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. A000292, A001788, A053016, A063925, A130809.

Cf. A359201 (edges), A359662 (cells).

Formula

{a(n), n >= 1} = {{12, 96, 720, 1200} U {A000292} U {A001788} U {A130809}} \ {0, 1}.