Barth Sextic is a algebraic surface of degree 6. Its formula is:

4*(ϕ^2*x^2-y^2)*(ϕ^2*y^2-z^2)*(ϕ^2*z^2-x^2)-(1+2*ϕ)*(x^2+y^2+z^2-w^2)^2 * w^2 == 0

where ϕ is the golden ratio (ϕ = (1 + Sqrt[5])/2 ≈ 1.61803) and w is the parameter. In the above plot, w=1.

When w is 0, the surface is 6 intersecting planes, arranged in a way like 2 tall-x-crossed planes intersecting from 3 mutually orthogonal directions.