A377752 Decimal expansion of the circumradius of a truncated icosahedron with unit edge length.

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

Offset

1,1

Links

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

Polytope Wiki, Truncated icosahedron.

Eric Weisstein's World of Mathematics, Truncated Icosahedron.

Wikipedia, Truncated icosahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt(58 + 18*sqrt(5))/4 = sqrt(58 + 18*A002163)/4.

Minimal polynomial: 16*x^4 - 116*x^2 + 109. - Amiram Eldar, May 17 2026

Example

2.47801865906761553756640791226630780693649473...

Mathematica

First[RealDigits[Sqrt[58 + 18*Sqrt[5]]/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedIcosahedron", "Circumradius"], 10, 100]]

Prog

(PARI) sqrt(58 + 18*sqrt(5))/4 \\ Charles R Greathouse IV, Feb 05 2025

Crossrefs

Cf. A377750 (surface area), A377751 (volume), A205769 (midradius + 1), A377787 (Dehn invariant).

Cf. A019881 (analogous for a regular icosahedron).

Cf. A002163.

Sequence in context: A063034 A351745 A094541 * A166928 A237199 A335192

Adjacent sequences: A377749 A377750 A377751 * A377753 A377754 A377755

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 07 2024

Status

approved