A387149 Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated square pyramid (Johnson solid J_10).

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

Offset

1,1

Comments

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

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

Links

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

Wikipedia, Gyroelongated square bipyramid.

Wikipedia, Gyroelongated square pyramid.

Formula

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

Example

2.2261954369024298095991888315497640747046712455090...

Mathematica

First[RealDigits[ArcCos[(1 - Sqrt[8])/3], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J10", "DihedralAngles"]], 2], 10, 100]]

Crossrefs

Cf. other J_10 dihedral angles: A156546, A387148, A387150.

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

Cf. A010466.

Sequence in context: A270380 A241460 A167568 * A361301 A240501 A278251

Adjacent sequences: A387146 A387147 A387148 * A387150 A387151 A387152

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 19 2025

Status

approved