A387610 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

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

Offset: 1

Author

Paolo Xausa, Sep 05 2025

Keywords

• nonn
• cons
• easy
• new

Comments

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

Also the analogous dihedral angle in a gyroelongated pentagonal rotunda (Johnson solid J_25).

Also the analogous dihedral angle in a decagonal antiprism.

Examples

			1.662367547590761895478403159830360396768735377275...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Polytope Wiki, Decagonal antiprism.
• Polytope Wiki, Gyroelongated pentagonal cupola.
• Polytope Wiki, Gyroelongated pentagonal rotunda.
• Wikipedia, Gyroelongated pentagonal cupola.
• Wikipedia, Gyroelongated pentagonal rotunda.

Crossrefs

Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387608, A387609.

Cf. A384283 (J_24 volume), A384284 (J_24 surface area).

Cf. A384285 (J_25 volume), A384286 (J_25 surface area).

Cf. A002163, A002194, A010476, A195693, A386852.

Programs

Mathematica

First[RealDigits[ArcCos[(Sqrt[5 + Sqrt[20]] - Sqrt[5] - 1)/Sqrt[3]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J24", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).

Equals A387608 - A386852.

Equals A387609 - A195693.