A389281 Decimal expansion of the largest dihedral angle, in radians, in an augmented truncated dodecahedron (Johnson solid J_68).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face and a square face at the edge where the pentagonal cupola (Johnson solid J_5) and truncated dodecahedron parts of the solid meet.

Also the analogous dihedral angle in a parabiaugmented truncated dodecahedron, metabiaugmented truncated dodecahedron and triaugmented truncated dodecahedron (Johnson solids J_69, J_70 and J_71, respectively).

Links

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

Polytope Wiki, Augmented truncated dodecahedron.

Polytope Wiki, Metabiaugmented truncated dodecahedron.

Polytope Wiki, Parabiaugmented truncated dodecahedron.

Polytope Wiki, Triaugmented truncated dodecahedron.

Wikipedia, Augmented truncated dodecahedron.

Wikipedia, Metabiaugmented truncated dodecahedron.

Wikipedia, Parabiaugmented truncated dodecahedron.

Wikipedia, Triaugmented truncated dodecahedron.

Formula

Equals arccos(-sqrt((23 + 3*sqrt(5))/30)) = arccos(-sqrt((23 + A010499)/30)).

Example

3.0428088727024703039757854817249488298668853021128...

Mathematica

First[RealDigits[ArcCos[-Sqrt[(23 + Sqrt[45])/30]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J68", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_68 dihedral angles: A137218, A344075, A377995, A377996, A389851.

Cf. A386464 (J_68 volume), A386465 (J_68 surface area).

Cf. A386466 (J_69 and J_70 volume), A386543 (J_69 and J_70 surface area).

Cf. A386544 (J_71 volume), A386545 (J_71 surface area).

Cf. A010499.

Sequence in context: A113486 A108572 A322335 * A245907 A104686 A301428

Adjacent sequences: A389278 A389279 A389280 * A389282 A389283 A389284

Keyword

nonn,cons,easy

Author

Paolo Xausa, Oct 27 2025

Status

approved