A378823 Decimal expansion of the surface area of a pentagonal icositetrahedron with unit shorter edge length.

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

Offset

2,1

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Eric Weisstein's World of Mathematics, Pentagonal Icositetrahedron.

Wikipedia, Pentagonal icositetrahedron.

Formula

Equals 24*(1 + s)^2*(2 + 3*s)/(1 + 2*s)*sqrt((1 - s)/(1 + s)), where s = (A058265 - 1)/2.

Equals the positive real root of x^6 - 3060*x^4 + 185328*x^2 - 39517632.

Example

54.79654943865969339763502315259019090870864439852...

Mathematica

First[RealDigits[Root[#^6 - 3060*#^4 + 185328*#^2 - 39517632 &, 2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalIcositetrahedron", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A378824 (volume), A378825 (inradius), A378826 (midradius), A378827 (dihedral angle).

Cf. A377602 (surface area of a snub cube with unit edge length).

Cf. A058265.

Sequence in context: A333203 A340705 A252666 * A245073 A021650 A141269

Adjacent sequences: A378820 A378821 A378822 * A378824 A378825 A378826

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 09 2024

Status

approved