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

Author

Paolo Xausa, Dec 14 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			2.8032178560848059621034493264877253281152659880354...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Triakis Icosahedron.
• Wikipedia, Triakis icosahedron.

Crossrefs

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

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

Cf. A002163.

Programs

Mathematica

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

Formula

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