A379134 Decimal expansion of the inradius of a pentakis dodecahedron with unit shorter edge length.

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

Offset

1,2

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.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt(477/436 + 97*sqrt(5)/218) = sqrt(477/436 + 97*A002163/218).

Equals the largest root of 1744*x^4 - 3816*x^2 + 361.

Example

1.4453319256522148283158512491020811977238711778430...

Mathematica

First[RealDigits[Sqrt[477/436 + 97*Sqrt[5]/218], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentakisDodecahedron", "Inradius"], 10, 100]]

Prog

(PARI) sqrt(477/436 + 97*sqrt(5)/218) \\ Charles R Greathouse IV, Feb 05 2025

Crossrefs

Cf. A379132 (surface area), A379133 (volume), A379135 (midradius), A379136 (dihedral angle).

Cf. A002163.

Sequence in context: A179778 A307983 A330305 * A011333 A283268 A016709

Adjacent sequences: A379131 A379132 A379133 * A379135 A379136 A379137

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 17 2024

Status

approved