A387323 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

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

Offset

1,2

Comments

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

Links

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

Polytope Wiki, Gyroelongated square cupola.

Wikipedia, Gyroelongated square cupola.

Formula

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

Equals A387321 - A195696 = A387322 - A003881.

Example

1.6858923822495302658575939503353780784364569832448...

Mathematica

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

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387321, A387322.

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

Cf. A002193, A003881, A010487, A195696.

Sequence in context: A296845 A392146 A030644 * A319032 A344125 A073462

Adjacent sequences: A387320 A387321 A387322 * A387324 A387325 A387326

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 29 2025

Status

approved