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

1,1

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.

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.

Index entries for transcendental numbers

Formula

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

Example

2.7783286661990213551074289190050780042508333364090...

Mathematica

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

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.

Sequence in context: A021040 A246553 A330479 * A349804 A388186 A355500

Adjacent sequences: A387604 A387605 A387606 * A387608 A387609 A387610

Keyword

nonn,cons,easy

Author

Paolo Xausa, Sep 04 2025

Status

approved