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

Author

Amiram Eldar, Jun 02 2023

Keywords

• nonn
• cons

Examples

			2.78516386312262296729255491273594698789932177207633...
		

Links

• Eric Weisstein's World of Mathematics, Regular Dodecahedron.
• Wikipedia, Regular dodecahedron.
• Index entries for algebraic numbers, degree 4.

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.

Programs

Mathematica

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

PARI

2*sqrt(5+sqrt(5))/sqrt(27) \\ Charles R Greathouse IV, Feb 07 2025

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.