A378977 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a triakis icosahedron.

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

Offset

1,1

Comments

The triakis icosahedron is the dual polyhedron of the truncated dodecahedron.

Links

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

Eric Weisstein's World of Mathematics, Triakis Icosahedron.

Wikipedia, Triakis icosahedron.

Formula

Equals arccos(-3*(8 + 5*sqrt(5))/61 = arccos(-3*(8 + 5*A002163)/61.

Example

2.8032178560848059621034493264877253281152659880354...

Mathematica

First[RealDigits[ArcCos[-3*(8 + 5*Sqrt[5])/61], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["TriakisIcosahedron", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. A378973 (surface area), A378974 (volume), A378975 (inradius), A378976 (midradius).

Cf. A137218 and A344075 (dihedral angles of a truncated dodecahedron).

Cf. A002163.

Sequence in context: A010594 A370944 A093588 * A369499 A016593 A020818

Adjacent sequences: A378974 A378975 A378976 * A378978 A378979 A378980

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 14 2024

Status

approved