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A063723 Number of vertices in the Platonic solids (in the order tetrahedron, cube, octahedron, dodecahedron, icosahedron). 18

%I #21 Nov 05 2020 22:01:56

%S 4,8,6,20,12

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

%C 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

%C 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

%C 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

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

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

%Y Cf. A053012, A053016, A060296, A060852.

%Y Cf. A165922 (tetrahedron), A049541 (octahedron), A165952 (cube), A165954 (icosahedron), A165953 (dodecahedron). - _Rick L. Shepherd_, Oct 04 2009

%Y Cf. A234974. - _Jens Voß_, Jan 02 2014

%K easy,fini,full,nonn

%O 1,1

%A _Henry Bottomley_, Aug 14 2001

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)