A389930 Decimal expansion of the largest dihedral angle, in radians, in an augmented tridiminished icosahedron (Johnson solid J_64).

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

Offset

1,1

Comments

This is the dihedral angle between a triangular face and a pentagonal face at the edge where the regular tetrahedron and the tridiminished icosahedron (Johnson solid J_63) parts of the solid meet.

Links

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

Polytope Wiki, Augmented tridiminished icosahedron.

Wikipedia, Augmented tridiminished icosahedron.

Formula

Equals arccos(-sqrt((5 - 2*sqrt(5))/15)) + arccos(1/3) = A389109 + A137914.

Example

2.9904662749192333711473852700703469901456955747195...

Mathematica

First[RealDigits[ArcCos[-Sqrt[(5 - Sqrt[20])/15]] + ArcCos[1/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J64", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_64 dihedral angles: A105199, A137914, A236367, A389109.

Cf. A386002 (J_64 volume), A386003 (J_64 surface area).

Sequence in context: A379827 A348637 A104954 * A244292 A011072 A175295

Adjacent sequences: A389927 A389928 A389929 * A389931 A389932 A389933

Keyword

nonn,cons,easy

Author

Paolo Xausa, Oct 20 2025

Status

approved