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

Author

Paolo Xausa, Jan 07 2025

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			3.49952784890576408257539390033789827877584936895...
		

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.

Crossrefs

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

Programs

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]]

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.