A389931 Decimal expansion of the largest dihedral angle, in radians, in an augmented truncated tetrahedron (Johnson solid J_65).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face and a square face at the edge where the triangular cupola (Johnson solid J_3) and truncated tetrahedron parts of the solid meet.

Links

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

Polytope Wiki, Augmented truncated tetrahedron.

Wikipedia, Augmented truncated tetrahedron.

Formula

Equals arccos(-5*sqrt(3)/9) = arccos(-5*A020784).

Example

2.8659498543735278344915713075472732627302440850300...

Mathematica

First[RealDigits[ArcCos[-5/Sqrt[27]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J65", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_65 dihedral angles: A137914, A156546, A195698, A386435.

Cf. A386411 (J_65 volume), A386412 (J_65 surface area).

Cf. A020784.

Sequence in context: A021353 A377997 A131361 * A228042 A382599 A239386

Adjacent sequences: A389928 A389929 A389930 * A389932 A389933 A389934

Keyword

nonn,cons,easy

Author

Paolo Xausa, Oct 23 2025

Status

approved