A377806 Decimal expansion of the circumradius of a snub dodecahedron with unit edge length.

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

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Snub Dodecahedron.

Wikipedia, Snub dodecahedron.

Index entries for algebraic numbers, degree 12.

Formula

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

Equals the real root closest to 2 of 4096*x^12 - 27648*x^10 + 47104*x^8 - 35776*x^6 + 13872*x^4 -2696*x^2 + 209.

Example

2.1558373751156397018366290766930582770168512187748...

Mathematica

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

Crossrefs

Cf. A377804 (surface area), A377805 (volume), A377807 (midradius).

Cf. A179296 (analogous for a regular dodecahedron).

Cf. A377849.

Sequence in context: A152290 A248699 A032006 * A167158 A074392 A284428

Adjacent sequences: A377803 A377804 A377805 * A377807 A377808 A377809

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 10 2024

Status

approved