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

Author

Paolo Xausa, Jan 09 2025

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			3.59762482255118901142825655944442353841196452...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pentagonal Hexecontahedron.
• Wikipedia, Pentagonal hexecontahedron.

Crossrefs

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

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

Programs

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]]

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.