A390979 Decimal expansion of the fourth largest dihedral angle, in radians, in a hebesphenomegacorona (Johnson solid J_89).

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

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 = -0.780878762... is the second smallest real root of 104976*x^10 + 262440*x^9 + 125145*x^8 - 329832*x^7 - 588708*x^6 - 278280*x^5 + 318294*x^4 + 438248*x^3 + 109452*x^2 - 44576*x - 14759.

Example

2.4668676438641974340297434598615814357127463717421...

Mathematica

First[RealDigits[ArcCos[Root[104976*#^10 + 262440*#^9 + 125145*#^8 - 329832*#^7 - 588708*#^6 - 278280*#^5 + 318294*#^4 + 438248*#^3 + 109452*#^2 - 44576*# - 14759 &, 2]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J89", "DihedralAngles"]], 4], 10, 100]]

Crossrefs

Cf. other J_89 dihedral angles: A390975, A390976, A390977, A390978, A390980, A390981, A390982.

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

Sequence in context: A339743 A131450 A114218 * A133691 A111973 A349787

Adjacent sequences: A390976 A390977 A390978 * A390980 A390981 A390982

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 01 2025

Status

approved