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 $(\pm 1,\pm 1,0)$. The six planes $x=\pm 1$, $y=\pm 1$, $z=\pm 1$ cut out the square faces; the eight planes $\pm x\pm y\pm z=2$ cut out the triangular faces. All edges have length $\sqrt{2}$. 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.