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I am looking for linear equation systems for the construction of standard polyhedra in 3 dimensions. I found another one beside the simple cube, the Cuboctahedron:

x <= 1
y <= 1
z <= 1
x + y + z <= 2.5
x + y - z <= 1.5
-x + y + z <= 1.5
x - y + z <= 1.5
x - y - z <= 0.5
-x - y + z <= 0.5
-x + y - z <= 0.5
-x - y - z <= -0.5
x >= 0
y >= 0
z >= 0

Results in:

Cuboctahedron

I am also interested:
- tetrahedron
- octahedron
- dodecahedron
- icosahedron
Do you know the systems of equations for any of these?

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