A380002 Decimal expansion of long/short edge length ratio of a pentagonal hexecontahedron.

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

Offset: 1

Author

Paolo Xausa, Jan 11 2025

Keywords

• nonn
• cons
• easy

Examples

			1.749852566736202791676446693655921179649815818590...
		

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), A379890 (midradius), A379892 (dihedral angle), A380003 and A380004 (face internal angles).

Cf. A377849.

Programs

Mathematica

First[RealDigits[(1 + #)/(2 - #^2) & [Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1]], 10, 100]] (* or *)
First[RealDigits[1/Divide @@ PolyhedronData["PentagonalHexecontahedron", "EdgeLengths"], 10, 100]]

Formula

Equals (1 + xi)/(2 - xi^2), where xi = A377849.

Equals the largest real root of 31*x^6 - 122*x^5 + 177*x^4 - 128*x^3 + 51*x^2 - 11*x + 1.