A387321 Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

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

Offset: 1

Author

Paolo Xausa, Aug 27 2025

Keywords

• nonn
• cons
• easy
• new

Comments

This is the dihedral angle between adjacent triangular faces 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).

Examples

			2.6412090003740395440214510528511358326798716782548...
		

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.

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387322, A387323.

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

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

Cf. A002193, A010487, A195696.

Programs

Mathematica

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

Formula

Equals arcsec(sqrt(3)) + arccos(-sqrt((7 + 4*sqrt(2) - 2*sqrt(20 + 14*sqrt(2)))/3)) = A195696 + arccos(-sqrt((7 + A010487 - 2*sqrt(20 + 14*A002193))/3)).

Equals A195696 + A387323.