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A387608

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

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

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OFFSET

1,1

COMMENTS

This is the dihedral angle between adjacent triangular faces 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 arccos(sqrt((5 + 2*sqrt(5))/15)) + arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = arccos(sqrt((5 + A010476)/15)) + arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).

Equals A386852 + A387610.

EXAMPLE

2.314725687375130081473793791474182971134043297238...

MATHEMATICA

First[RealDigits[ArcSec[Sqrt[15 - 6*#]] + ArcCos[(Sqrt[5 + 2*#] - # - 1)/Sqrt[3]] & [Sqrt[5]], 10, 100]] (* or *)

First[RealDigits[RankedMax[Union[PolyhedronData["J24", "DihedralAngles"]], 4], 10, 100]]

CROSSREFS

Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387609, 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, A386852.