A378976 Decimal expansion of the midradius of a triakis icosahedron with unit shorter edge length.

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

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 2.

Formula

Equals 1/2 + 2/sqrt(5) = 1/2 + 2/A002163.

Equals (A249600 + 13)/10 = (A010532 + 5)/10.

Minimal polynomial: 20*x^2 - 20*x - 11. - Amiram Eldar, Jun 09 2026

Example

1.3944271909999158785636694674925104941762473438446...

Mathematica

First[RealDigits[1/2 + 2/Sqrt[5], 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "Midradius"], 10, 100]]

Crossrefs

Cf. A378973 (surface area), A378974 (volume), A378975 (inradius), A378977 (dihedral angle).

Cf. A377697 (midradius of a truncated dodecahedron with unit edge length).

Cf. A002163, A010532, A249600.

Sequence in context: A321120 A243711 A247553 * A388405 A307238 A161773

Adjacent sequences: A378973 A378974 A378975 * A378977 A378978 A378979

Keyword

nonn,cons,easy,changed

Author

Paolo Xausa, Dec 14 2024

Status

approved