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

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

Author

Paolo Xausa, Aug 19 2025

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			1.81228288299223868132256212312198395270891707198...
		

Links

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

Crossrefs

Cf. other J_10 dihedral angles: A156546, A387148, A387149.

Cf. A179638 (J_10 volume), A374948 (J_10 surface area).

Cf. A010466.

Programs

Mathematica

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

Formula

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