A387191 -id:A387191 - cp's OEIS frontend

A386530 Decimal expansion of the largest dihedral angle, in radians, in an elongated pentagonal rotunda (Johnson solid J_21).

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

Offset: 1

Paolo Xausa, Aug 22 2025

This is the dihedral angle between a triangular face and a square face (at the edge where the prism and rotunda parts of the solid meet).

Also the analogous dihedral angle in Johnson solids J_40-J_43.

			2.9528821228062311686815089830968947118603985336982...

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

Cf. other J_21 dihedral angles: A019669, A228824, A344075, A387191.
Cf. A384213 (J_21 volume), A179637 (J_21 surface area - 10).
Cf. A002163.

First[RealDigits[ArcCos[-Sqrt[2*(5 + Sqrt[5])/15]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J21", "DihedralAngles"]], 10, 100]]

Equals arccos(-sqrt(2*(5 + sqrt(5))/15)) = arccos(-sqrt(2*(5 + A002163)/15)).

cp's OEIS Frontend

A386530 Decimal expansion of the largest dihedral angle, in radians, in an elongated pentagonal rotunda (Johnson solid J_21).

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