Cartesian Coordinates
Cartesian coordinates for the vertices of a snub cube are all the even permutations of
- (±1, ±ξ, ±1/ξ)
with an even number of plus signs, along with all the odd permutations with an odd number of plus signs, where ξ is the real solution to
which can be written
or approximately 0.543689. ξ is the reciprocal of the tribonacci constant. Taking the even permutations with an odd number of plus signs, and the odd permutations with an even number of plus signs, gives a different snub cube, the mirror image.
This snub cube has edges of length α, a number which satisfies the equation
and can be written as
For a snub cube with unit edge length, use the following coordinates (with all the even permutation) instead:
Read more about this topic: Snub Cube