A378826 - OEIS

A378826

Decimal expansion of the midradius of a pentagonal icositetrahedron with unit shorter edge length.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The pentagonal icositetrahedron is the dual polyhedron of the snub cube.

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..10000

FORMULA

Equals (1 + s)/sqrt(2*(1 + s)*(1 - 2*s)), where s = (A058265 - 1)/2.

Equals the positive real root of 32*x^6 - 144*x^4 + 12*x^2 - 1.

EXAMPLE

2.101593893296299757309517286375546687971276345216...

MATHEMATICA

First[RealDigits[Root[32*#^6 - 144*#^4 + 12*#^2 - 1 &, 2], 10, 100]] (* or *)

First[RealDigits[PolyhedronData["PentagonalIcositetrahedron", "Midradius"], 10, 100]]

CROSSREFS

Cf. A378823 (surface area), A378824 (volume), A378825 (inradius), A378827 (dihedral angle).

Cf. A377605 (midradius of a snub cube with unit edge length).

Cf. A058265.

Sequence in context: A151824 A275514 A180782 * A213597 A302978 A108723

Adjacent sequences: A378823 A378824 A378825 * A378827 A378828 A378829

KEYWORD

nonn,cons,easy

AUTHOR

Paolo Xausa, Dec 10 2024

STATUS

approved