A391147 Decimal expansion of the third smallest dihedral angle, in radians, in a disphenocingulum (Johnson solid J_90).

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

Offset

1,1

Links

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

Polytope Wiki, Disphenocingulum.

Wikipedia, Disphenocingulum.

Formula

Equals arccos(c), where c = -0.68950815... is the fourth smallest real root of 59049*x^12 - 78732*x^11 - 826686*x^10 + 726084*x^9 + 3206871*x^8 - 1246104*x^7 - 5492772*x^6 - 522072*x^5 + 4074471*x^4 + 1878564*x^3 - 653438*x^2 - 495596*x - 39815.

Example

2.331606072422299399658811235073899733903659223306...

Mathematica

First[RealDigits[ArcCos[Root[59049*#^12 - 78732*#^11 - 826686*#^10 + 726084*#^9 + 3206871*#^8 - 1246104*#^7 - 5492772*#^6 - 522072*#^5 + 4074471*#^4 + 1878564*#^3 - 653438*#^2 - 495596*# - 39815 &, 4]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J90", "DihedralAngles"]], 3], 10, 100]]

Crossrefs

Cf. other J_90 dihedral angles: A391145, A391146, A391148, A391149, A391150, A391151.

Cf. A386752 (J_90 volume), A385257 (J_90 surface area + 2).

Sequence in context: A298599 A138677 A193885 * A364957 A076239 A019798

Adjacent sequences: A391144 A391145 A391146 * A391148 A391149 A391150

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 08 2025

Status

approved