A387295 Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated triangular cupola (Johnson solid J_22).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face in the antiprism part of the solid and a square 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(sqrt(3)/3) + arccos(1 - 2*sqrt(3)/3) = A195696 + arccos(-A246724).

Example

2.6814372804191827475908005056128080315848833860639...

Mathematica

First[RealDigits[ArcTan[Sqrt[2]] + ArcCos[1 - Sqrt[12]/3], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J22", "DihedralAngles"]], 2], 10, 100]]

Crossrefs

Cf. other J_22 dihedral angles: A195698, A387294, A387296, A387297.

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

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

Cf. A195696, A246724.

Sequence in context: A327279 A021377 A261875 * A084686 A040164 A086353

Adjacent sequences: A387292 A387293 A387294 * A387296 A387297 A387298

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 25 2025

Status

approved