A384284 -id:A384284 - cp's OEIS frontend

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

Paolo Xausa, Sep 05 2025

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).

			2.2159419064878071469869358899196289168037591999759...

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.

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.

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]]

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.

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

Original entry on oeis.org

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

Paolo Xausa, Sep 05 2025

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.

			1.662367547590761895478403159830360396768735377275...

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.

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.

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

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.

cp's OEIS Frontend

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

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