A387608 Decimal expansion of the fourth largest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

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

Offset: 1

Author

Paolo Xausa, Sep 04 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 pentagonal bicupola and gyroelongated pentagonal cupolarotunda (Johnson solids J_46 and J_47, respectively).

Examples

			2.314725687375130081473793791474182971134043297238...
		

Links

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

Crossrefs

Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387609, A387610.

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

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

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

Cf. A002163, A002194, A010476, A386852.

Programs

Mathematica

First[RealDigits[ArcSec[Sqrt[15 - 6*#]] + ArcCos[(Sqrt[5 + 2*#] - # - 1)/Sqrt[3]] & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J24", "DihedralAngles"]],4], 10, 100]]

Formula

Equals arccos(sqrt((5 + 2*sqrt(5))/15)) + arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = arccos(sqrt((5 + A010476)/15)) + arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).

Equals A386852 + A387610.