A379133 Decimal expansion of the volume of a pentakis dodecahedron with unit shorter edge length.

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

Offset

2,2

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.

Wikipedia, Pentakis dodecahedron.

Index entries for algebraic numbers, degree 2.

Formula

Equals (5/36)*(41 + 25*sqrt(5)) = (5/36)*(41 + 25*A002163).

Example

13.458569366318714223642964127539153595279924859762...

Mathematica

First[RealDigits[5/36*(41 + 25*Sqrt[5]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentakisDodecahedron", "Volume"], 10, 100]]

Prog

(PARI) (41 + 25*sqrt(5))*5/36 \\ Charles R Greathouse IV, Feb 05 2025

Crossrefs

Cf. A379132 (surface area), A379134 (inradius), A379135 (midradius), A379136 (dihedral angle).

Cf. A377751 (volume of a truncated icosahedron with unit edge length).

Cf. A002163.

Sequence in context: A269719 A214626 A143593 * A364089 A028267 A364063

Adjacent sequences: A379130 A379131 A379132 * A379134 A379135 A379136

Keyword

nonn,cons,easy,changed

Author

Paolo Xausa, Dec 16 2024

Status

approved