A232811 - OEIS

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A232811

Decimal expansion of the surface index of a regular octahedron.

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

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OFFSET

1,1

COMMENTS

Equivalently, the surface area of a regular octahedron with unit volume. Among Platonic solids, surface indices decrease with increasing number of faces: A232812 (tetrahedron), 6.0 (cube = hexahedron), this one, A232810 (dodecahedron), and A232809 (icosahedron).

An algebraic integer of degree 6 with minimal polynomial x^6 - 34992. - 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 6

FORMULA

sqrt(3)*6^(2/3).

A010469/A131594^(2/3).

EXAMPLE

5.7191057579816194425444539723965629466374425679...

MATHEMATICA

RealDigits[Sqrt[3]Surd[36, 3], 10, 120][[1]] (* Harvey P. Dale, Mar 12 2015 *)