A063723 Number of vertices in the Platonic solids (in the order tetrahedron, cube, octahedron, dodecahedron, icosahedron).

4, 8, 6, 20, 12

Offset: 1

Author

Henry Bottomley, Aug 14 2001

Keywords

• easy
• fini
• full
• nonn

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 cross-references 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

Examples

			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

Formula

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