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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?

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1 Answer 1

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.

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