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

1,1

Comments

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

Links

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

Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.

Wikipedia, Pentakis dodecahedron.

Formula

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

Example

2.7352547614903346619898560183934957927169693...

Mathematica

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

Prog

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

Crossrefs

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

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

Cf. A002163.

Sequence in context: A326661 A326662 A345038 * A345237 A011049 A372131

Adjacent sequences: A379133 A379134 A379135 * A379137 A379138 A379139

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 17 2024

Status

approved