A377807 Decimal expansion of the midradius of a snub dodecahedron with unit edge length.

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

Offset: 1

Author

Paolo Xausa, Nov 10 2024

Keywords

• nonn
• cons
• easy

Examples

			2.0970538352520879924039590523482862400308397305810...
		

Links

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

Crossrefs

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

Cf. A239798 (analogous for a regular dodecahedron).

Cf. A377849.

Programs

Mathematica

First[RealDigits[Sqrt[1/(1 - Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1])]/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["SnubDodecahedron", "Midradius"], 10, 100]]

Formula

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

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.