A387322 Decimal expansion of the fourth largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face and a square face at the edge where the antiprism and cupola parts of the solid meet.

Also the analogous dihedral angle in a gyroelongated square bicupola (Johnson solid J_45).

Links

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

Polytope Wiki, Gyroelongated square bicupola.

Polytope Wiki, Gyroelongated square cupola.

Wikipedia, Gyroelongated square bicupola.

Wikipedia, Gyroelongated square cupola.

Formula

Equals Pi/4 + arccos(-sqrt((7 + 4*sqrt(2) - 2*sqrt(20 + 14*sqrt(2)))/3)) = A003881 + arccos(-sqrt((7 + A010487 - 2*sqrt(20 + 14*A002193))/3)).

Equals A003881 + A387323.

Example

2.4712905456469785754732547961552537994857493330886...

Mathematica

First[RealDigits[Pi/4 + ArcCos[-Sqrt[(7 + Sqrt[32] - 2*Sqrt[20 + 14*Sqrt[2]])/3]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J23", "DihedralAngles"]], 4], 10, 100]]

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387321, A387323.

Cf. A384214 (J_23 volume), A384215 (J_23 surface area).

Cf. A385258 (J_45 volume), A385259 (J_45 surface area).

Cf. A003881, A002193, A010487.

Sequence in context: A097879 A180658 A019748 * A061501 A272001 A395605

Adjacent sequences: A387319 A387320 A387321 * A387323 A387324 A387325

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 29 2025

Status

approved