A390977 Decimal expansion of the third smallest dihedral angle, in radians, in a hebesphenomegacorona (Johnson solid J_89).

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

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Polytope Wiki, Hebesphenomegacorona.

Wikipedia, Hebesphenomegacorona.

Formula

Equals arccos(c), where c = -0.622459754... is the second smallest real root of 688905*x^10 + 1089126*x^9 - 1343547*x^8 - 2466936*x^7 + 521154*x^6 + 1552932*x^5 + 355554*x^4 + 150408*x^3 - 42827*x^2 - 259994*x - 97319.

Example

2.24267796326912131461359535269464328172351232958...

Mathematica

First[RealDigits[ArcCos[Root[688905*#^10 + 1089126*#^9 - 1343547*#^8 - 2466936*#^7 + 521154*#^6 + 1552932*#^5 + 355554*#^4 + 150408*#^3 - 42827*#^2 - 259994*# - 97319 &, 2]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J89", "DihedralAngles"]], 3], 10, 100]]

Crossrefs

Cf. other J_89 dihedral angles: A390975, A390976, A390978, A390979, A390980, A390981, A390982.

Cf. A386741 (J_89 volume), A386742 (J_89 surface area).

Sequence in context: A062170 A375386 A307536 * A248842 A286538 A275331

Adjacent sequences: A390974 A390975 A390976 * A390978 A390979 A390980

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 28 2025

Status

approved