A377806 - OEIS

%I #11 Feb 11 2025 14:39:21

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

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

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

%N Decimal expansion of the circumradius of a snub dodecahedron with unit edge length.

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Snub_dodecahedron">Snub dodecahedron</a>.

%H <a href="/index/Al#algebraic_12">Index entries for algebraic numbers, degree 12</a>.

%F Equals sqrt(1 + 1/(1 - A377849))/2.

%F Equals the real root closest to 2 of 4096*x^12 - 27648*x^10 + 47104*x^8 - 35776*x^6 + 13872*x^4 -2696*x^2 + 209.

%e 2.1558373751156397018366290766930582770168512187748...

%t First[RealDigits[Sqrt[1 + 1/(1 - Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1])]/2, 10, 100]] (* or *)

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

%Y Cf. A377804 (surface area), A377805 (volume), A377807 (midradius).

%Y Cf. A179296 (analogous for a regular dodecahedron).

%Y Cf. A377849.

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Nov 10 2024