A387294 Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated triangular cupola (Johnson solid J_22).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face in the antiprism part of the solid and a triangular face in the cupola part of the solid.

Also the analogous dihedral angle in a gyroelongated triangular bicupola (Johnson solid J_44).

Links

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

Wikipedia, Gyroelongated triangular bicupola.

Wikipedia, Gyroelongated triangular cupola.

Formula

Equals arccos(1/3) + arccos(1 - 2*sqrt(3)/3) = A137914 + arccos(-A246724).

Example

2.9570800796354481515618725813450376530518087004...

Mathematica

First[RealDigits[ArcSec[3] + ArcCos[1 - Sqrt[12]/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J22", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_22 dihedral angles: A195698, A387295, A387296, A387297.

Cf. A344076 (J_22 volume), A344077 (J_22 surface area).

Cf. A385256 (J_44 volume), A385257 (J_44 surface area).

Cf. A137914, A246724.

Sequence in context: A051491 A339204 A253169 * A375509 A373495 A339925

Adjacent sequences: A387291 A387292 A387293 * A387295 A387296 A387297

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 25 2025

Status

approved