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

1,1

Links

Table of n, a(n) for n=1..90.

Eric Weisstein's World of Mathematics, Snub Dodecahedron.

Wikipedia, Snub dodecahedron.

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.

Example

2.0970538352520879924039590523482862400308397305810...

Mathematica

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

Crossrefs

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

Cf. A239798 (analogous for a regular dodecahedron).

Cf. A377849.

Sequence in context: A021481 A372910 A029686 * A083864 A154937 A037996

Adjacent sequences: A377804 A377805 A377806 * A377808 A377809 A377810

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 10 2024

Status

approved