A379888 Decimal expansion of the surface area of a pentagonal hexecontahedron with unit shorter edge length.

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

Offset

3,2

Comments

The pentagonal hexecontahedron is the dual polyhedron of the snub dodecahedron.

Links

Paolo Xausa, Table of n, a(n) for n = 3..10000

Eric Weisstein's World of Mathematics, Pentagonal Hexecontahedron.

Wikipedia, Pentagonal hexecontahedron.

Index entries for algebraic numbers, degree 12.

Formula

Equals 30*(2 + 3*t)*sqrt(1 - t^2)/(1 - 2*t^2), where t = ((44 + 12*A001622*(9 + sqrt(81*A001622 - 15)))^(1/3) + (44 + 12*A001622*(9 - sqrt(81*A001622 - 15)))^(1/3) - 4)/12.

Equals the largest real root of 961*x^12 - 33925050*x^10 + 238487439375*x^8 - 374285139187500*x^6 + 215543322643359375*x^4 - 200764566730722656250*x^2 + 19088214930090087890625.

Example

162.69896419846662676872582412137959709718223664038...

Mathematica

First[RealDigits[Root[961*#^12 - 33925050*#^10 + 238487439375*#^8 - 374285139187500*#^6 + 215543322643359375*#^4 - 200764566730722656250*#^2 + 19088214930090087890625 &, 8], 10, 100]]  (* or *)
First[RealDigits[PolyhedronData["PentagonalHexecontahedron", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A379889 (volume), A379890 (inradius), A379891 (midradius), A379892 (dihedral angle).

Cf. A377804 (surface area of a snub dodecahedron with unit edge length).

Cf. A001622.

Sequence in context: A369884 A388809 A195474 * A021945 A002371 A048595

Adjacent sequences: A379885 A379886 A379887 * A379889 A379890 A379891

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jan 07 2025

Status

approved