A387149 -id:A387149 - cp's OEIS frontend

A387148 Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated square pyramid (Johnson solid J_10).

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

Offset: 1

Paolo Xausa, Aug 19 2025

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

Also the analogous dihedral angle in a gyroelongated square bipyramid (Johnson solid J_17).

			2.76759950111674795948641922563774170695233176699...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Gyroelongated square bipyramid.
Wikipedia, Gyroelongated square pyramid.

Cf. other J_10 dihedral angles: A156546, A387149, A387150.
Cf. A179638 (J_10 volume), A374948 (J_10 surface area).
Cf. A002193, A011027.

First[RealDigits[ArcCos[(1 - Sqrt[2] - 32^(1/4))/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J10", "DihedralAngles"]], 10, 100]]

Equals arccos((1 - sqrt(2) - 2*2^(1/4))/3) = arccos((1 - A002193 - A011027)/3).

A387150 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated square pyramid (Johnson solid J_10).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 19 2025

This is the dihedral angle between the square face and a triangular face.

			1.81228288299223868132256212312198395270891707198...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Gyroelongated square pyramid.

Cf. other J_10 dihedral angles: A156546, A387148, A387149.
Cf. A179638 (J_10 volume), A374948 (J_10 surface area).
Cf. A010466.

First[RealDigits[ArcCos[-Sqrt[1 - Sqrt[8]/3]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J10", "DihedralAngles"]], 10, 100]]

Equals arccos(-sqrt(1 - 2*sqrt(2)/3)) = arccos(-sqrt(1 - A010466/3)).

cp's OEIS Frontend

A387148 Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated square pyramid (Johnson solid J_10).

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