A387190 Decimal expansion of the second smallest dihedral angle, in radians, in an elongated pentagonal cupola (Johnson solid J_20).

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

Offset

1,1

Comments

This is the dihedral angle between adjacent square faces at the edge where the prism and cupola parts of the solid meet.

Also the analogous dihedral angle in Johnson solids J_38-J_41.

Also the dihedral angle between a square face and a decagonal face in Johnson solids J_76-J_83.

Links

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

Wikipedia, Elongated pentagonal cupola.

Formula

Equals arccos(-sqrt((5 - sqrt(5))/10)) = arccos(-sqrt((5 - A002163)/10)).

Example

2.124370685691941870739854421729019962133608522388...

Mathematica

First[RealDigits[ArcCos[-Sqrt[(5 - Sqrt[5])/10]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J20", "DihedralAngles"]], 2], 10, 100]]

Crossrefs

Cf. other J_20 dihedral angles: A019669, A228824, A377995, A377996, A387147.

Cf. A384144 (J_20 volume), A179591 (J_20 surface area - 10).

Cf. A002163.

Sequence in context: A187500 A323460 A129144 * A360594 A295313 A105022

Adjacent sequences: A387187 A387188 A387189 * A387191 A387192 A387193

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 22 2025

Status

approved