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

Author

Paolo Xausa, Dec 17 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			1.4453319256522148283158512491020811977238711778430...
		

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.

Crossrefs

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

Cf. A002163.

Programs

Mathematica

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

PARI

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

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.