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A232809 Decimal expansion of the surface index of a regular icosahedron. 9
5, 1, 4, 8, 3, 4, 8, 5, 5, 6, 1, 9, 9, 5, 1, 5, 6, 4, 6, 3, 3, 0, 8, 1, 2, 9, 4, 6, 1, 1, 6, 0, 1, 9, 0, 6, 4, 1, 0, 0, 8, 6, 4, 1, 1, 6, 3, 8, 6, 7, 2, 4, 1, 4, 8, 4, 5, 0, 7, 1, 3, 6, 7, 5, 3, 9, 8, 0, 3, 2, 4, 7, 9, 0, 5, 0, 8, 5, 7, 7, 1, 3, 0, 2, 9, 8, 3, 7, 3, 2, 5, 6, 2, 9, 9, 4, 3, 1, 0, 9, 6, 7, 4, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, surface area of a regular icosahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: A232812 (tetrahedron), 6.0 (cube = hexahedron), A232811 (octahedron), A232810 (dodecahedron), and this one.

An algebraic integer of degree 12 with minimal polynomial x^12 - 41115600x^6 + 765275040000 \\ Charles R Greathouse IV, Apr 25 2016

LINKS

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

Wikipedia, Platonic solid

FORMULA

5*sqrt(3)/(5*(3+sqrt(5))/12)^(2/3).

10*A010527/A102208^(2/3).

EXAMPLE

5.14834855619951564633081294611601906410086411638672414845...

PROG

(PARI) 5*sqrt(3)/(5*(3+sqrt(5))/12)^(2/3) \\ Charles R Greathouse IV, Apr 25 2016

CROSSREFS

Cf. A010527, A102208 (solid index of a sphere), A232808, A232810, A232811, A232812.

Sequence in context: A216851 A179290 A167864 * A011301 A180132 A286593

Adjacent sequences:  A232806 A232807 A232808 * A232810 A232811 A232812

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, Dec 01 2013

STATUS

approved

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Last modified August 22 01:16 EDT 2017. Contains 290942 sequences.