A377752 - OEIS

%I #8 Feb 05 2025 10:23:52

%S 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,

%T 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,

%U 9,5,7,7,1,2,0,7,4,2,1,6,7,6,1,8,4,2,6,2,2,0

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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TruncatedIcosahedron.html">Truncated Icosahedron</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Truncated_icosahedron">Truncated icosahedron</a>.

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.

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

%e 2.47801865906761553756640791226630780693649473...

%t First[RealDigits[Sqrt[58 + 18*Sqrt[5]]/4, 10, 100]] (* or *)

%t First[RealDigits[PolyhedronData["TruncatedIcosahedron", "Circumradius"], 10, 100]]

%o (PARI) sqrt(58 + 18*sqrt(5))/4 \\ _Charles R Greathouse IV_, Feb 05 2025

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

%Y Cf. A019881 (analogous for a regular icosahedron).

%Y Cf. A002163.

%K nonn,cons,easy,changed

%O 1,1

%A _Paolo Xausa_, Nov 07 2024