A359662 Number of (3-dimensional) cells of regular m-polytopes for m >= 3.

1, 5, 8, 15, 16, 24, 35, 40, 70, 80, 120, 126, 160, 210, 240, 330, 495, 560, 600, 715, 1001, 1120, 1365, 1792, 1820, 2016, 2380, 3060, 3360, 3876, 4845, 5280, 5376, 5985, 7315, 7920, 8855, 10626, 11440, 12650, 14950, 15360, 16016, 17550, 20475, 21840, 23751

Offset

1,2

Comments

In 3 dimensions there are five (convex) regular polytopes and each of them (trivially) consists of a single cell.

In 4 dimensions there are six regular 4-polytopes and they have 5, 8, 16, 24, 120, 600 3-dimensional cells (A063924).

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 (3-dimensional) cells in ascending order and define the present sequence.

Links

Table of n, a(n) for n=1..47.

MathStackExchange, MathStackExchange discussion concerning the number of edges of convex regular n-polytopes

Wikipedia, List of regular polytopes and compounds

Formula

Equals {{24, 120, 600} U {A000332} U {A001789} U {A130810}} \ {0}.

Example

8 is a term since the hypersurface of a tesseract consists of 8 (cubical) cells.

Crossrefs

Cf. A000332, A001789, A063924, A130810.

Cf. A359201 (edges), A359202 (faces).

Sequence in context: A112269 A314527 A314528 * A091574 A314529 A314530

Adjacent sequences: A359659 A359660 A359661 * A359663 A359664 A359665

Keyword

easy,nonn

Author

Marco Ripà, Jan 10 2023

Status

approved