A379890 Decimal expansion of the inradius of a pentagonal hexecontahedron with unit shorter edge length.

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

Index entries for algebraic numbers, degree 12.

Formula

Equals the largest real root of 856064*x^12 - 11107328*x^10 + 7691264*x^8 - 698816*x^6 + 8816*x^4 - 440*x^2 + 1.

Example

3.49952784890576408257539390033789827877584936895...

Mathematica

First[RealDigits[Root[856064*#^12 - 11107328*#^10 + 7691264*#^8 - 698816*#^6 + 8816*#^4 - 440*#^2 + 1 &, 8], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalHexecontahedron", "Inradius"], 10, 100]]

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379891 (midradius), A379892 (dihedral angle).

Sequence in context: A306018 A076120 A082188 * A202499 A341319 A063780

Adjacent sequences: A379887 A379888 A379889 * A379891 A379892 A379893

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jan 07 2025

Status

approved