A179451 Decimal expansion of the surface area of an icosidodecahedron with side length 1.

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

Offset

2,1

Comments

Icosidodecahedron: 32 faces, 30 vertices, and 60 edges.

Also the surface area of a pentagonal orthobirotunda (Johnson solid J_34) with unit edges. - Paolo Xausa, Oct 03 2025

Links

Table of n, a(n) for n=2..106.

Polytope Wiki, Icosidodecahedron.

Eric Weisstein's World of Mathematics, Icosidodecahedron.

Wikipedia, Icosidodecahedron.

Index entries for algebraic numbers, degree 8.

Formula

Equals Sqrt(30*(10+3*sqrt(5)+sqrt(75+30*sqrt(5)))).

Minimal polynomial: x^8 - 1200*x^6 + 324000*x^4 - 27000000*x^2 + 324000000. - Amiram Eldar, May 24 2026

Example

29.3059828449119895407453754361926770276025163091742830907641713815460...

Mathematica

RealDigits[N[Sqrt[30*(10+3*Sqrt[5]+Sqrt[75+30*Sqrt[5]])], 200]]

Prog

(PARI) polrootsreal(x^8 - 1200*x^6 + 324000*x^4 - 27000000*x^2 + 324000000)[8] \\ Charles R Greathouse IV, Oct 30 2023

Crossrefs

Cf. A010527, A102208, A179290, A179292, A179294, A179449, A179450.

Sequence in context: A345299 A276048 A339203 * A124918 A395472 A348763

Adjacent sequences: A179448 A179449 A179450 * A179452 A179453 A179454

Keyword

nonn,cons,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 14 2010

Extensions

Partially rewritten by Charles R Greathouse IV, Feb 03 2011

Status

approved