A232810 Decimal expansion of the surface index of a regular dodecahedron.

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

Offset

1,1

Comments

Equivalently, the surface area of a regular dodecahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: A232812 (tetrahedron), 6.0 (cube = hexahedron), A232811 (octahedron), this one, and A232809 (icosahedron).

An algebraic integer with degree 12 and minimal polynomial x^12 - 18954000x^6 + 425152800000. - Charles R Greathouse IV, Apr 25 2016

Links

Stanislav Sykora, Table of n, a(n) for n = 1..1000

Wikipedia, Platonic solid.

Index entries for algebraic numbers, degree 12

Formula

Equals 3*sqrt(25+10*sqrt(5))/((15+7*sqrt(5))/4)^(2/3).

Equals A131595/A102769^(2/3).

Example

5.311613997069083669796666701461086337809888399341493422663761...

Mathematica

RealDigits[3*Sqrt[25 + 10*Sqrt[5]]/((15 + 7*Sqrt[5])/4)^(2/3), 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)

Prog

(PARI) 3*sqrt(25+10*sqrt(5))/((15+7*sqrt(5))/4)^(2/3) \\ Charles R Greathouse IV, Apr 25 2016

Crossrefs

Cf. A102769, A131595, A232808 (surface index of a sphere), A232809, A232811, A232812.

Sequence in context: A097527 A204063 A132400 * A063268 A179613 A196613

Adjacent sequences: A232807 A232808 A232809 * A232811 A232812 A232813

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Dec 01 2013

Status

approved