A390633 Decimal expansion of the fourth smallest dihedral angle, in radians, in a sphenomegacorona (Johnson solid J_88).

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

Offset

1,1

Links

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

Polytope Wiki, Sphenomegacorona.

Wikipedia, Sphenomegacorona.

Formula

Equals arccos(c), where c = -0.635331... is the largest negative real root of 9685512225*x^16 + 44768589840*x^15 + 27052472664*x^14 - 108235399824*x^13 - 39626366724*x^12 + 258070583952*x^11 + 28999672488*x^10 - 417343530384*x^9 - 51960351258*x^8 + 365161430448*x^7 + 43492752360*x^6 - 182102664240*x^5 - 14991112260*x^4 + 49819609008*x^3 + 1699340184*x^2 - 5718379440*x + 102988225.

Example

2.259233905911399368823445978405373811624799200521...

Mathematica

First[RealDigits[ArcCos[Root[9685512225*#^16 + 44768589840*#^15 + 27052472664*#^14 - 108235399824*#^13 - 39626366724*#^12 + 258070583952*#^11 + 28999672488*#^10 - 417343530384*#^9 - 51960351258*#^8 + 365161430448*#^7 + 43492752360*#^6 - 182102664240*#^5 - 14991112260*#^4 + 49819609008*#^3 + 1699340184*#^2 - 5718379440*# + 102988225 &, 4]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J88", "DihedralAngles"]], 4], 10, 100]]

Crossrefs

Cf. other J_88 dihedral angles: A390630, A390631, A390632, A390634, A390635, A390636, A390637, A390638.

Cf. A334114 (J_88 volume), A010502 (J_88 surface area - 2).

Sequence in context: A208938 A019086 A076949 * A040009 A227527 A275504

Adjacent sequences: A390630 A390631 A390632 * A390634 A390635 A390636

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 20 2025

Status

approved