A387607 Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

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

Offset: 1

Author

Paolo Xausa, Sep 04 2025

Keywords

• nonn
• cons
• easy
• new

Comments

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

Also the analogous dihedral angle in a gyroelongated pentagonal rotunda, gyroelongated pentagonal bicupola, gyroelongated pentagonal cupolarotunda and gyroelongated pentagonal birotunda (Johnson solids J_25, J_46, J_47 and J_48, respectively).

Also the analogous dihedral angle in a decagonal antiprism.

Examples

			2.7783286661990213551074289190050780042508333364090...
		

Links

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

Crossrefs

Cf. other J_24 dihedral angles: A377995, A377996, A387608, A387609, A387610.

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

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

Cf. A385260 (J_46 volume), A385261 (J_46 surface area).

Cf. A385262 (J_47 volume), A385263 (J_47 surface area).

Cf. A385264 (J_48 volume), A385488 (J_48 surface area).

Cf. A010476.

Programs

Mathematica

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

Formula

Equals arccos((1 - sqrt(10 + 2*sqrt(5)))/3) = arccos((1 - sqrt(10 + A010476))/3).