Coordinates for vertices of the "silver" rhombohedron. The "silver" rhombohedron (a.k.a the trigonal trapezohedron) is a three-dimensional object with six faces composed of congruent rhombi. You can see it visualised here. 
I am interested in replicating the visualisation linked to above in MATLAB, but to do that I need to know the coordinates of the rhombohedron's eight vertices (I am using the patch function).
How do I calculate the coordinates of the vertices of the silver rhombohedron?

Use vectors $e_1=(1,0,0)$, $e_2=(\cos{\alpha},\sin{\alpha},0)$ and $e_3=(\cos{\alpha},0,\sin{\alpha})$ as basis.
Then vertices are set of all points with each coordinate $0$ or $1$: $(0,0,0)$, $(0,0,1)$, ..., $(1,1,1)$.
Or $0$, $e_1$, $e_2$, $e_3$, $e_1+e_2$, ..., $e_1+e_2+e_3$.
Multiply coordinates by constant if needed.
