A377805 Decimal expansion of the volume of a snub dodecahedron with unit edge length.

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

Offset: 2

Author

Paolo Xausa, Nov 09 2024

Keywords

• nonn
• cons
• easy

Examples

			37.616649962733362975777673671302714340355289873...
		

Links

• Eric Weisstein's World of Mathematics, Snub Dodecahedron.
• Wikipedia, Snub dodecahedron.
• Index entries for algebraic numbers, degree 12.

Crossrefs

Cf. A377804 (surface area), A377806 (circumradius), A377807 (midradius).

Cf. A102769 (analogous for a regular dodecahedron).

Cf. A001622, A090550, A104457, A134946, A377849.

Programs

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]]

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 largest real root of 2176782336*x^12 - 3195335070720*x^10 + 162223191936000*x^8 + 1030526618040000*x^6 + 6152923794150000*x^4 - 182124351550575000*x^2 + 187445810737515625.