A378975 Decimal expansion of the inradius of a triakis icosahedron with unit shorter edge length.

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

Offset

1,2

Comments

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

Links

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

Polytope Wiki, Triakis icosahedron.

Eric Weisstein's World of Mathematics, Triakis Icosahedron.

Wikipedia, Triakis icosahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt((477 + 199*sqrt(5))/488) = sqrt((477 + 199*A002163)/488).

Minimal polynomial: 976*x^4 - 1908*x^2 + 121. - Amiram Eldar, Jun 09 2026

Example

1.37451744701047164727510000639742367448102733307...

Mathematica

First[RealDigits[Sqrt[(477 + 199*Sqrt[5])/488], 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "Inradius"], 10, 100]]

Crossrefs

Cf. A378973 (surface area), A378974 (volume), A378976 (midradius), A378977 (dihedral angle).

Cf. A002163.

Sequence in context: A267412 A087941 A278389 * A021271 A388528 A238274

Adjacent sequences: A378972 A378973 A378974 * A378976 A378977 A378978

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 14 2024

Status

approved