A377807 - OEIS

%I #7 Nov 11 2024 08:10:06

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

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

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

%N Decimal expansion of the midradius 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>.

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

%F Equals the real root closest to 2 of 4096*x^12 - 21504*x^10 + 16384*x^8 - 4672*x^6 + 624*x^4 - 40*x^2 + 1.

%e 2.0970538352520879924039590523482862400308397305810...

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

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

%Y Cf. A377804 (surface area), A377805 (volume), A377806 (circumradius).

%Y Cf. A239798 (analogous for a regular dodecahedron).

%Y Cf. A377849.

%K nonn,cons,easy

%O 1,1

%A _Paolo Xausa_, Nov 10 2024