A379136 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentakis dodecahedron.

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

Offset: 1

Author

Paolo Xausa, Dec 17 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			2.7352547614903346619898560183934957927169693...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.
• Wikipedia, Pentakis dodecahedron.

Crossrefs

Cf. A379132 (surface area), A379133 (volume), A379134 (inradius), A379135 (midradius).

Cf. A236367 and A344075 (dihedral angles of a truncated icosahedron).

Cf. A002163.

Programs

Mathematica

First[RealDigits[ArcCos[-(80 + 9*Sqrt[5])/109], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["PentakisDodecahedron", "DihedralAngles"]], 10, 100]]

PARI

acos(-(80 + 9*sqrt(5))/109) \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals arccos(-(80 + 9*sqrt(5))/109) = arccos(-(80 + 9*A002163)/109).