A389932 Decimal expansion of the largest dihedral angle, in radians, in an augmented truncated cube (Johnson solid J_66).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face and a square face at the edge where the square cupola (Johnson solid J_4) and truncated cube parts of the solid meet.

Also the analogous dihedral angle in a biaugmented truncated cube (Johnson solid J_67).

Links

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

Polytope Wiki, Augmented truncated cube.

Polytope Wiki, Biaugmented truncated cube.

Wikipedia, Augmented truncated cube.

Wikipedia, Biaugmented truncated cube.

Formula

Equals arccos(-1/sqrt(3) - 1/sqrt(6)) = arccos(-A020760 - A020763).

Example

2.9716741988627322699144471265836208510030470542...

Mathematica

First[RealDigits[ArcCos[-1/Sqrt[3] - 1/Sqrt[6]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J66", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_66 dihedral angles: A019669, A177870, A195698, A195702.

Cf. A386459 (J_66 volume), A386460 (J_66 surface area).

Cf. A010524 (J_67 volume - 9), A386461 (J_67 surface area).

Cf. A020760, A020763.

Sequence in context: A197017 A094044 A357109 * A011070 A230480 A393777

Adjacent sequences: A389929 A389930 A389931 * A389933 A389934 A389935

Keyword

nonn,cons,easy

Author

Paolo Xausa, Oct 24 2025

Status

approved