A390175 Decimal expansion of the second smallest dihedral angle, in radians, in a snub square antiprism (Johnson solid J_85).

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

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 = -0.8104878... is the largest negative root of 81*x^6 - 54*x^5 - 513*x^4 + 492*x^3 + 367*x^2 - 246*x + 1.

Example

2.51578077546136803693663507701290853162140127962...

Mathematica

First[RealDigits[ArcCos[Root[81*#^6 - 54*#^5 - 513*#^4 + 492*#^3 + 367*#^2 - 246*# + 1 &, 2]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J85", "DihedralAngles"]], 2], 10, 100]]

Crossrefs

Cf. other J_85 dihedral angles: A390174, A390176, A390177.

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

Sequence in context: A258020 A021803 A388367 * A356273 A077382 A046527

Adjacent sequences: A390172 A390173 A390174 * A390176 A390177 A390178

Keyword

nonn,cons,easy

Author

Paolo Xausa, Oct 29 2025

Status

approved