OFFSET
2,1
LINKS
Eric Weisstein's World of Mathematics, Snub Dodecahedron.
Wikipedia, Snub dodecahedron.
FORMULA
Equals ((3*phi + 1)*xi*(xi + 1) - phi/6 - 2)/sqrt(3*xi^2 - phi^2) = (A090550*xi*(xi + 1) - A134946 - 2)/sqrt(3*xi^2 - A104457), where phi = A001622 and xi = A377849.
Equals the real root closest to 37 of 2176782336*x^12 - 3195335070720*x^10 + 162223191936000*x^8 + 1030526618040000*x^6 + 6152923794150000*x^4 - 182124351550575000*x^2 + 187445810737515625.
EXAMPLE
37.616649962733362975777673671302714340355289873...
MATHEMATICA
First[RealDigits[((3*GoldenRatio + 1)*#*(# + 1) - GoldenRatio/6 - 2)/Sqrt[3*#^2 - GoldenRatio^2], 10, 100]] & [Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1]] (* or *)
First[RealDigits[PolyhedronData["SnubDodecahedron", "Volume"], 10, 100]]
CROSSREFS
Cf. A102769 (analogous for a regular dodecahedron).
KEYWORD
AUTHOR
Paolo Xausa, Nov 09 2024
STATUS
approved