A390982 Decimal expansion of the largest dihedral angle, in radians, in a hebesphenomegacorona (Johnson solid J_89).

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

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 = -0.921512... is the smallest real root of 6561*x^10 - 4374*x^9 - 19683*x^8 + 9720*x^7 + 18954*x^6 - 5076*x^5 - 3942*x^4 - 1896*x^3 - 1499*x^2 + 1786*x + 25.

Example

2.742752598649779495835415794588923937718309958347...

Mathematica

First[RealDigits[ArcCos[Root[6561*#^10 - 4374*#^9 - 19683*#^8 + 9720*#^7 + 18954*#^6 - 5076*#^5 - 3942*#^4 - 1896*#^3 - 1499*#^2 + 1786*# + 25 &, 1]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J89", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_89 dihedral angles: A390975, A390976, A390977, A390978, A390979, A390980, A390981.

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

Sequence in context: A073239 A134882 A125140 * A257345 A110637 A092943

Adjacent sequences: A390979 A390980 A390981 * A390983 A390984 A390985

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 01 2025

Status

approved