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

Author

Stanislav Sykora, Dec 01 2013

Keywords

• nonn
• cons
• easy

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

Examples

			5.311613997069083669796666701461086337809888399341493422663761...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..1000
• Wikipedia, Platonic solid.
• Index entries for algebraic numbers, degree 12

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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

Equals A131595/A102769^(2/3).