A377750 - OEIS

%I #14 Feb 05 2025 10:12:45

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

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

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

%N Decimal expansion of the surface area 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_08">Index entries for algebraic numbers, degree 8</a>.

%F Equals 3*(10*sqrt(3) + sqrt(25 + 10*sqrt(5))) = 30*A002194 + 3*sqrt(25 + 10*A002163).

%F Equals 30*(A002194 + A375067).

%e 72.60725303413392187893153397383948620117264765443...

%t First[RealDigits[3*(10*Sqrt[3] + Sqrt[25 + Sqrt[500]]), 10, 100]] (* or *)

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

%o (PARI) 3*(10*sqrt(3) + sqrt(25 + 10*sqrt(5))) \\ _Charles R Greathouse IV_, Feb 05 2025

%Y Cf. A377751 (volume), A377752 (circumradius), A205769 (midradius + 1), A377787 (Dehn invariant).

%Y Cf. A010527 (analogous for a regular icosahedron, with offset 1).

%Y Cf. A002163, A002194, A375067.

%K nonn,cons,easy,changed

%O 2,1

%A _Paolo Xausa_, Nov 06 2024