A378715 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a disdyakis dodecahedron.

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

Offset

1,1

Comments

The disdyakis dodecahedron is the dual polyhedron of the truncated cuboctahedron (great rhombicuboctahedron).

Links

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

Wikipedia, Disdyakis dodecahedron.

Index entries for transcendental numbers.

Formula

Equals arccos(-(71 + 12*sqrt(2))/97) = arccos(-(71 + 12*A002193)/97).

Example

2.7066946454792287856258644383068280456984454555717...

Mathematica

First[RealDigits[ArcCos[-(71 + 12*Sqrt[2])/97], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DisdyakisDodecahedron", "DihedralAngles"]], 10, 100]]

Prog

(PARI) acos(-(71 + 12*sqrt(2))/97) \\ Charles R Greathouse IV, Oct 10 2025

Crossrefs

Cf. A378712 (surface area), A378713 (volume), A378714 (inradius), A378393 (midradius).

Cf. A177870, A195698 and A195702 (dihedral angles of a truncated cuboctahedron (great rhombicuboctahedron)).

Cf. A002193.

Sequence in context: A343049 A098198 A021791 * A325905 A372386 A199273

Adjacent sequences: A378712 A378713 A378714 * A378716 A378717 A378718

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 07 2024

Status

approved