A387670 Decimal expansion of the second largest dihedral angle, in radians, in an augmented triangular prism (Johnson solid J_49).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face and a square face at the edge where the pyramid and prism parts of the solid meet.

Also the analogous dihedral angle in a biaugmented triangular prism (Johnson solid J_50).

Links

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

Polytope Wiki, Augmented triangular prism.

Polytope Wiki, Biaugmented triangular prism.

Wikipedia Augmented triangular prism.

Wikipedia Biaugmented triangular prism.

Index entries for transcendental numbers.

Formula

Equals arccos((sqrt(3) - 3*sqrt(2))/6) = arccos((A002194 - A010474)/6).

Example

2.0025141693211070243180715636089253823091378281350...

Mathematica

First[RealDigits[ArcCos[(Sqrt[3] - 3*Sqrt[2])/6], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J49", "DihedralAngles"]], 2], 10, 100]]

Prog

(PARI) acos((sqrt(3)-sqrt(18))/6) \\ Charles R Greathouse IV, Oct 07 2025

Crossrefs

Cf. other J_49 dihedral angles: A019669, A019670, A156546, A195702.

Cf. A384139 (J_49 volume), A104956 (J_49 surface area - 2).

Cf. A002194, A010474.

Sequence in context: A223142 A244522 A292945 * A024690 A200728 A066209

Adjacent sequences: A387667 A387668 A387669 * A387671 A387672 A387673

Keyword

nonn,cons,easy

Author

Paolo Xausa, Oct 06 2025

Status

approved