Voozh

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

(list; constant; graph; refs; listen; history; text; internal format)

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