A377603 Decimal expansion of the volume of a snub cube (snub cuboctahedron) with unit edge length.

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

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Snub Cube.

Wikipedia, Snub cube.

Index entries for algebraic numbers, degree 6.

Formula

Equals (8*A058265 + 6)/(3*sqrt(2*(A058265^2 - 3))).

Equals sqrt((613*A058265 + 203)/(315*A058265 - 558)).

Example

7.8894773999753902064510142704428061847387079829...

Mathematica

First[RealDigits[(8*# + 6)/(3*Sqrt[2*(#^2 - 3)]), 10, 100]] & [Root[#^3 - #^2 - # - 1 &, 1]] (* or *)
First[RealDigits[PolyhedronData["SnubCube", "Volume"], 10, 100]]

Prog

(PARI) polrootsreal(729*x^6 - 45684*x^4 + 19386*x^2 - 12482)[2] \\ Charles R Greathouse IV, Feb 11 2025

Crossrefs

Cf. A377602 (surface area), A377604 (circumradius), A377605 (midradius).

Cf. A058265.

Sequence in context: A099987 A226320 A021563 * A333938 A268575 A198814

Adjacent sequences: A377600 A377601 A377602 * A377604 A377605 A377606

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 02 2024

Status

approved