login
A359201
Number of edges of regular m-polytopes for m >= 3.
2
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
1,1
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.
FORMULA
{a(n), n >= 1} = {{30, 96, 720} U {A000217} U {A001787} U {A046092}} \ {0, 1, 3, 4}.
EXAMPLE
6 is a term since a tetrahedron has 6 edges.
CROSSREFS
Cf. A359202 (faces), A359662 (cells).
Sequence in context: A297366 A325472 A305188 * A270364 A359029 A315123
KEYWORD
easy,nonn
AUTHOR
Marco Ripà, Dec 20 2022
STATUS
approved