A387609 Decimal expansion of the fifth largest (second smallest) dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face and a square face 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).

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.

Formula

Equals arctan(2)/2 + arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = A195693 + arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).

Equals A195693 + A387610.

Example

2.2159419064878071469869358899196289168037591999759...

Mathematica

First[RealDigits[ArcTan[2]/2 + ArcCos[(Sqrt[5 + Sqrt[20]] - Sqrt[5] - 1)/Sqrt[3]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J24", "DihedralAngles"]], 5], 10, 100]]

Crossrefs

Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387608, 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, A195693.

Sequence in context: A380616 A380615 A329429 * A326617 A371727 A326962

Adjacent sequences: A387606 A387607 A387608 * A387610 A387611 A387612

Keyword

nonn,cons,easy

Author

Paolo Xausa, Sep 05 2025

Status

approved