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

1,2

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 (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.

Example

1.749852566736202791676446693655921179649815818590...

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]]

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379890 (midradius), A379892 (dihedral angle), A380003 and A380004 (face internal angles).

Cf. A377849.

Sequence in context: A117028 A138282 A198572 * A155823 A195452 A103227

Adjacent sequences: A379999 A380000 A380001 * A380003 A380004 A380006

Keyword

nonn,cons,easy,new

Author

Paolo Xausa, Jan 11 2025

Status

approved