Wikipedia
Hemi-cuboctahedron
A hemi-cuboctahedron is an abstract polyhedron, containing half the faces of a semiregular cuboctahedron.
It has 4 triangular faces and 3 square faces, 12 edges, and 6 vertices. It can be seen as a rectified hemi-octahedron or rectified hemi-cube.
It can be realized as a projective polyhedron (a tessellation of the real projective plane by 4 triangles and 3 square), which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected.