A179292 Decimal expansion of radius of inscribed sphere of a regular icosahedron with radius of circumscribed sphere = 1.

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

Offset

0,1

Comments

Icosahedron: A three-dimensional figure with 20 equilateral triangle faces, 12 vertices, and 30 edges.

Links

Table of n, a(n) for n=0..104.

Dr. Math, Icosahedron.

Polytope Wiki, Icosahedron.

Eric Weisstein's World of Mathematics, Regular Icosahedron.

Wikipedia, Regular icosahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt(75 + 30*sqrt(5))/15.

Minimal polynomial: 45*x^4 - 30*x^2 + 1. - Amiram Eldar, May 19 2026

Example

0.794654472291766122955530928327594042026590588309264801754955775008438...

Mathematica

R=1; RealDigits[N[(Sqrt[75+30*Sqrt[5]]/15)*R, 175]]

Prog

(PARI) polrootsreal(45*x^4-30*x^2+1)[4] \\ Charles R Greathouse IV, Sep 02 2024
(PARI) sqrt(6/sqrt(5)+3)/3 \\ Charles R Greathouse IV, Sep 02 2024

Crossrefs

Cf. A010527, A102208, A179290.

Sequence in context: A386742 A303296 A118270 * A361972 A395844 A198756

Adjacent sequences: A179289 A179290 A179291 * A179293 A179294 A179295

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 09 2010

Extensions

Offset corrected, keyword:cons added by R. J. Mathar, Jul 11 2010

Status

approved