A390975 Decimal expansion of the smallest dihedral angle, in radians, in a hebesphenomegacorona (Johnson solid J_89).

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

Offset

1,2

Links

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

Polytope Wiki, Hebesphenomegacorona.

Wikipedia, Hebesphenomegacorona.

Formula

Equals arccos(c), where c = -0.2168448... is the second smallest real root of 26880*x^10 - 35328*x^9 - 25600*x^8 + 39680*x^7 + 6112*x^6 - 13696*x^5 + 2128*x^4 + 1808*x^3 - 1119*x^2 - 494*x - 47.

Example

1.7893775422798726790542731973325771331938261057...

Mathematica

First[RealDigits[ArcCos[Root[26880*#^10 - 35328*#^9 - 25600*#^8 + 39680*#^7 + 6112*#^6 - 13696*#^5 + 2128*#^4 + 1808*#^3 - 1119*#^2 - 494*# - 47 &, 2]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J89", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_89 dihedral angles: A390976, A390977, A390978, A390979, A390980, A390981, A390982.

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

Sequence in context: A254272 A284363 A383057 * A114514 A011471 A257237

Adjacent sequences: A390972 A390973 A390974 * A390976 A390977 A390978

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 27 2025

Status

approved