A390634 Decimal expansion of the fifth largest dihedral angle, in radians, in a sphenomegacorona (Johnson solid J_88).

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

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 = -0.734205... is the fifth smallest real root of 11019960576*x^32 - 176319369216*x^30 + 1327293029376*x^28 - 6159749815296*x^26 + 19328874801408*x^24 - 42424671435264*x^22 + 65677619660544*x^20 - 72739172102400*x^18 + 65116400118624*x^16 - 67363076805120*x^14 + 81074000049984*x^12 - 74243471510592*x^10 + 42113235752208*x^8 - 13684531014432*x^6 + 2303754089616*x^4 - 160807989744*x^2 + 2655031729.

Example

2.3952913283035176420735149247744094127418260603870...

Mathematica

First[RealDigits[ArcCos[Root[11019960576*#^32 - 176319369216*#^30 + 1327293029376*#^28 - 6159749815296*#^26 + 19328874801408*#^24 - 42424671435264*#^22 + 65677619660544*#^20 - 72739172102400*#^18 + 65116400118624*#^16 - 67363076805120*#^14 + 81074000049984*#^12 - 74243471510592*#^10 + 42113235752208*#^8 - 13684531014432*#^6 + 2303754089616*#^4 - 160807989744*#^2 + 2655031729 &, 5]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J88", "DihedralAngles"]], 5], 10, 100]]

Crossrefs

Cf. other J_88 dihedral angles: A390630, A390631, A390632, A390633, A390635, A390636, A390637, A390638.

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

Sequence in context: A229212 A210586 A202017 * A127198 A065631 A222244

Adjacent sequences: A390631 A390632 A390633 * A390635 A390636 A390637

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 20 2025

Status

approved