A387147 -id:A387147 - cp's OEIS frontend

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

Paolo Xausa, Aug 22 2025

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.

			2.124370685691941870739854421729019962133608522388...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Elongated pentagonal cupola.

Cf. other J_20 dihedral angles: A019669, A228824, A377995, A377996, A387147.
Cf. A384144 (J_20 volume), A179591 (J_20 surface area - 10).
Cf. A002163.

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

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

cp's OEIS Frontend

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

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