A377798 Decimal expansion of the circumradius of a truncated icosidodecahedron (great rhombicosidodecahedron) with unit edge length.

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

Offset

1,1

Links

Table of n, a(n) for n=1..90.

Polytope Wiki, Great rhombicosidodecahedron.

Eric Weisstein's World of Mathematics, Great Rhombicosidodecahedron.

Wikipedia, Truncated icosidodecahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt(31/4 + 3*sqrt(5)) = sqrt(31/4 + A010499) = sqrt(31 + A344171)/2.

Minimal polynomial: 16*x^4 - 248*x^2 + 241. - Amiram Eldar, Jun 10 2026

Example

3.802394499851293584766836714110323209303892865251...

Mathematica

First[RealDigits[Sqrt[31/4 + Sqrt[45]], 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["TruncatedIcosidodecahedron", "Circumradius"], 10, 100]]

Crossrefs

Cf. A377796 (surface area), A377797 (volume), A377799 (midradius).

Cf. A010499, A344171.

Sequence in context: A155979 A120669 A021267 * A086106 A199731 A010626

Adjacent sequences: A377795 A377796 A377797 * A377799 A377800 A377801

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 08 2024

Status

approved