= Cuboctahedron
A <cuboctahedron> is a convex <uniform polyhedron> with eight equilateral triangular faces and six square faces. Around each of its twelve vertices the faces alternate triangle, square, triangle, square. It has twenty-four edges, and the <Euler characteristic> check is $12-24+14=2$.
A concrete model is the <convex hull> of all coordinate permutations of $(\pm1,\pm1,0)$. The six planes $x=\pm1$, $y=\pm1$, $z=\pm1$ cut out the square faces; the eight planes $\pm x\pm y\pm z=2$ cut out the triangular faces. All edges have length $\sqrt2$. Equivalently, join the midpoints of neighbouring edges of a <cube>: its vertices become triangular faces, and its faces become squares. The construction makes the name and the shared symmetries with the <cube> and <octahedron> visible.
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