A363438 Decimal expansion of the volume of the regular dodecahedron inscribed in the unit-radius sphere.

2, 7, 8, 5, 1, 6, 3, 8, 6, 3, 1, 2, 2, 6, 2, 2, 9, 6, 7, 2, 9, 2, 5, 5, 4, 9, 1, 2, 7, 3, 5, 9, 4, 6, 9, 8, 7, 8, 9, 9, 3, 2, 1, 7, 7, 2, 0, 7, 6, 3, 3, 1, 9, 9, 2, 6, 3, 7, 0, 2, 4, 1, 4, 7, 4, 1, 6, 2, 5, 5, 1, 5, 0, 3, 2, 9, 1, 0, 6, 4, 9, 3, 0, 9, 4, 4, 4, 8, 5, 1, 3, 4, 7, 6, 6, 4, 8, 0, 8, 8, 0, 6, 5, 4, 2

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Regular Dodecahedron.

Wikipedia, Regular dodecahedron.

Formula

Equals 2*sqrt(5+sqrt(5))/(3*sqrt(3)).

Equals 4*(phi+2)/(3*sqrt(3)), where phi is the golden ratio (A001622).

Equals A102769 / A179296 ^ 3.

Example

2.78516386312262296729255491273594698789932177207633...

Mathematica

RealDigits[(2*(5 + Sqrt[5]))/(3*Sqrt[3]), 10, 120][[1]]

Crossrefs

Cf. A118273 (cube), A122553 (regular octahedron), A339259 (regular icosahedron), A363437 (regular tetrahedron).

Cf. A001622.

Other constants related to the regular dodecahedron: A102769, A131595, A179296, A232810, A237603, A239798, A341906.

Sequence in context: A329406 A360441 A019731 * A021363 A352495 A141721

Adjacent sequences: A363435 A363436 A363437 * A363439 A363440 A363441

Keyword

nonn,cons

Author

Amiram Eldar, Jun 02 2023

Status

approved