A232809 Decimal expansion of the surface index of a regular icosahedron.

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

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.

Index entries for algebraic numbers, degree 12

Formula

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

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

Example

5.14834855619951564633081294611601906410086411638672414845...

Mathematica

RealDigits[5*Sqrt[3]/(5*(3+Sqrt[5])/12)^(2/3), 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)

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: A342014 A355953 A167864 * A011301 A316248 A180132

Adjacent sequences: A232806 A232807 A232808 * A232810 A232811 A232812

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Dec 01 2013

Status

approved