A387297 -id:A387297 - cp's OEIS frontend

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

Paolo Xausa, Aug 25 2025

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).

			2.9570800796354481515618725813450376530518087004...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Gyroelongated triangular bicupola.
Wikipedia, Gyroelongated triangular cupola.

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.

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

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

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

Original entry on oeis.org

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

Paolo Xausa, Aug 25 2025

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).

			2.6814372804191827475908005056128080315848833860639...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Gyroelongated triangular bicupola.
Wikipedia, Gyroelongated triangular cupola.

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.

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

Equals arccos(sqrt(3)/3) + arccos(1 - 2*sqrt(3)/3) = A195696 + arccos(-A246724).

A387296 Decimal expansion of the third largest dihedral angle, in radians, in a gyroelongated triangular cupola (Johnson solid J_22).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 26 2025

This is the dihedral angle between triangular faces in the antiprism part of the solid.

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

			2.5346001497151261930915028102102107021498303291935...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Gyroelongated triangular bicupola.
Wikipedia, Gyroelongated triangular cupola.

Cf. other J_22 dihedral angles: A195698, A387294, A387295, A387297.
Cf. A344076 (J_22 volume), A344077 (J_22 surface area).
Cf. A385256 (J_44 volume), A385257 (J_44 surface area).
Cf. A010469.

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

Equals arccos((1 - 2*sqrt(3))/3) = arccos((1 - A010469)/3).

cp's OEIS Frontend

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

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

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A387296 Decimal expansion of the third largest dihedral angle, in radians, in a gyroelongated triangular cupola (Johnson solid J_22).

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Mathematica

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