A389557 Decimal expansion of the largest dihedral angle, in radians, in an augmented hexagonal prism (Johnson solid J_54).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face and a square face.

Also the analogous dihedral angle in a parabiaugmented hexagonal prism, metabiaugmented hexagonal prism and triaugmented hexagonal prism (Johnson solids J_55, J_56 and J_57, respectively).

Links

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

Polytope Wiki, Augmented hexagonal prism.

Polytope Wiki, Metabiaugmented hexagonal prism.

Polytope Wiki, Parabiaugmented hexagonal prism.

Polytope Wiki, Triaugmented hexagonal prism.

Wikipedia, Augmented hexagonal prism.

Wikipedia, Metabiaugmented hexagonal prism.

Wikipedia, Parabiaugmented hexagonal prism.

Wikipedia, Triaugmented hexagonal prism.

Formula

Equals arctan(sqrt(2)) + (2/3)*Pi = A195696 + A019693.

Example

3.049711720517704770472286024702093010374860961260...

Mathematica

First[RealDigits[ArcTan[Sqrt[2]] + 2/3*Pi, 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J54", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_54 dihedral angles: A019669, A019693, A156546, A195702.

Cf. A385569 (J_54 volume), A354129 (J_54 surface area + 2).

Cf. A195696.

Sequence in context: A088230 A181482 A330420 * A072329 A068630 A374966

Adjacent sequences: A389554 A389555 A389556 * A389558 A389559 A389560

Keyword

nonn,cons,easy

Author

Paolo Xausa, Oct 14 2025

Status

approved