A386852 Decimal expansion of the dihedral angle, in radians, between the pentagonal face and a triangular face in a pentagonal pyramid with equal edges (Johnson solid J_2).

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

Offset

0,1

Comments

Also the dihedral angle, in radians, between the 10-gonal face and a triangular face in a pentagonal cupola (Johnson solid J_5)

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Wikipedia, Pentagonal cupola.

Wikipedia, Pentagonal pyramid.

Index entries for transcendental numbers.

Formula

Equals arcsec(sqrt(15 - 6*sqrt(5))) = arcsec(sqrt(15 - 6*A002163)).

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

Example

0.65235813978436818599539063164382257436530791996...

Mathematica

First[RealDigits[ArcSec[Sqrt[15 - 6*Sqrt[5]]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J2", "DihedralAngles"]], 10, 100]]

Prog

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

Crossrefs

Cf. A179552 (J_2 volume), A179553 (J_2 surface area).

Cf. A179590 (J_5 volume), A179591 (J_5 surface area).

Cf. A002163, A010476.

Sequence in context: A098866 A144689 A221215 * A199180 A197265 A198107

Adjacent sequences: A386849 A386850 A386851 * A386853 A386854 A386855

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 05 2025

Status

approved