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

1,2

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.

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.

Index entries for transcendental numbers

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.

Example

1.662367547590761895478403159830360396768735377275...

Mathematica

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

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.

Sequence in context: A021155 A395017 A254245 * A218387 A178857 A003676

Adjacent sequences: A387607 A387608 A387609 * A387611 A387612 A387613

Keyword

nonn,cons,easy

Author

Paolo Xausa, Sep 05 2025

Status

approved