

A063723


Number of vertices in the Platonic solids (in the order tetrahedron, cube, octahedron, dodecahedron, icosahedron).


18




OFFSET

1,1


COMMENTS

The preferred order for these five numbers is 4, 6, 8, 12, 20 (tetrahedron, octahedron, cube, icosahedron, dodecahedron), as in A053016.  N. J. A. Sloane, Nov 05 2020
Also number of faces of Platonic solids ordered by increasing ratios of volumes to their respective circumscribed spheres. See crossreferences for actual ratios.  Rick L. Shepherd, Oct 04 2009
Also the expected lengths of nontrivial random walks along the edges of a Platonic solid from one vertex back to itself.  Jens Voß, Jan 02 2014


LINKS

Table of n, a(n) for n=1..5.


FORMULA

a(n) = A063722(n)  A053016(n) + 2.


EXAMPLE

a(2) = 8 since a cube has eight vertices.


CROSSREFS

Cf. A053012, A053016, A060296, A060852.
Cf. A165922 (tetrahedron), A049541 (octahedron), A165952 (cube), A165954 (icosahedron), A165953 (dodecahedron).  Rick L. Shepherd, Oct 04 2009
Cf. A234974.  Jens Voß, Jan 02 2014
Sequence in context: A064494 A119800 A330685 * A323057 A028269 A019650
Adjacent sequences: A063720 A063721 A063722 * A063724 A063725 A063726


KEYWORD

easy,fini,full,nonn


AUTHOR

Henry Bottomley, Aug 14 2001


STATUS

approved



