A386853 Decimal expansion of the dihedral angle, in radians, between the 10-gonal face and a triangular face in a pentagonal rotunda (Johnson solid J_6).

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

Offset: 1

Author

Paolo Xausa, Aug 06 2025

Keywords

• nonn
• cons
• easy

Examples

			1.38208579601133454945018729145714326976181383401...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Pentagonal rotunda.
• Index entries for transcendental numbers.

Crossrefs

Cf. A179593 (volume), A179637 (surface area).

Cf. other J_6 dihedral angles: A105199, A344075.

Cf. A010476, A386852.

Programs

Mathematica

First[RealDigits[ArcCos[Sqrt[(5 - Sqrt[20])/15]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J6", "DihedralAngles"]], 2], 10, 100]]

PARI

acos(sqrt((5 - 2*sqrt(5))/15)) \\ Charles R Greathouse IV, Aug 19 2025

Formula

Equals arccos(sqrt((5 - 2*sqrt(5))/15)) = arccos(sqrt((5 - A010476)/15)).