A390174 Decimal expansion of the smallest dihedral angle, in radians, in a snub square antiprism (Johnson solid J_85).

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

Offset

1,1

Links

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

Polytope Wiki, Snub square antiprism.

Wikipedia, Snub square antiprism.

Formula

Equals arccos(c), where c = -0.416998... is the largest negative root of 729*x^6 - 7290*x^5 + 9315*x^4 + 5940*x^3 - 11565*x^2 + 558*x + 2297.

Example

2.0009363653497259345865481527474188752087664982691...

Mathematica

First[RealDigits[ArcCos[Root[729*#^6 - 7290*#^5 + 9315*#^4 + 5940*#^3 - 11565*#^2 + 558*# + 2297 &, 2]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J85", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_85 dihedral angles: A390175, A390176, A390177.

Cf. A386696 (J_85 volume), A385259 (J_85 surface area + 8).

Sequence in context: A169775 A329039 A365437 * A181502 A223154 A063698

Adjacent sequences: A390171 A390172 A390173 * A390175 A390176 A390177

Keyword

nonn,cons,easy

Author

Paolo Xausa, Oct 29 2025

Status

approved