A387770 - OEIS

A387770

Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated pentagonal rotunda (Johnson solid J_25).

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

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

OFFSET

1,1

COMMENTS

This is the dihedral angle between adjacent triangular faces at the edge where the antiprism and rotunda parts of the solid meet.

Also the analogous dihedral angle in a gyroelongated pentagonal cupolarotunda and gyroelongated pentagonal birotunda (Johnson solids J_47 and J_48, respectively).

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..10000

Polytope Wiki, Gyroelongated pentagonal birotunda.

Polytope Wiki, Gyroelongated pentagonal cupolarotunda.

Polytope Wiki, Gyroelongated pentagonal rotunda.

Wikipedia, Gyroelongated pentagonal birotunda.

Wikipedia, Gyroelongated pentagonal cupolarotunda.

Wikipedia, Gyroelongated pentagonal rotunda.

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 A386853 + A387610.

EXAMPLE

3.044453343602096444928590451287503666530549211...

MATHEMATICA

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

First[RealDigits[Max[PolyhedronData["J25", "DihedralAngles"]], 10, 100]]

CROSSREFS

Cf. other J_25 dihedral angles: A344075, A387607, A387610, A387771.

Cf. A384285 (J_25 volume), A384286 (J_25 surface area).

Cf. A385262 (J_47 volume), A385263 (J_47 surface area).

Cf. A385264 (J_48 volume), A385488 (J_48 surface area).

Cf. A002163, A002194, A010476, A386853.