A379891 Decimal expansion of the midradius of a pentagonal hexecontahedron with unit shorter edge length.

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

Offset

1,1

Comments

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

Links

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

Eric Weisstein's World of Mathematics, Pentagonal Hexecontahedron.

Wikipedia, Pentagonal hexecontahedron.

Formula

Equals the largest real root of 4096*x^12 - 58368*x^10 + 70656*x^8 - 17728*x^6 + 1392*x^4 - 120*x^2 + 1.

Example

3.59762482255118901142825655944442353841196452...

Mathematica

First[RealDigits[Root[4096*#^12 - 58368*#^10 + 70656*#^8 - 17728*#^6 + 1392*#^4 - 120*#^2 + 1 &, 8], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalHexecontahedron", "Midradius"], 10, 100]]

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379892 (dihedral angle).

Cf. A377807 (midradius of a snub dodecahedron with unit edge length).

Sequence in context: A016613 A336849 A348994 * A079427 A168271 A081761

Adjacent sequences: A379888 A379889 A379890 * A379892 A379893 A379894

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jan 09 2025

Status

approved