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A232810 Decimal expansion of the surface index of a regular dodecahedron. 9
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 (list; constant; graph; refs; listen; history; text; internal format)
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

FORMULA

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

A131595/A102769^(2/3).

EXAMPLE

5.311613997069083669796666701461086337809888399341493422663761...

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

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Last modified August 19 19:25 EDT 2017. Contains 290821 sequences.