It can be seen as an octahedron with triangular pyramids added to each face, and is also sometimes called a trisoctahedron, or, more fully, trigonal trisoctahedron.
It can be seen as an octahedron with triangular pyramids added to each face; that is, it is the Kleetope of the octahedron. It is also sometimes called a trisoctahedron, or, more fully, trigonal trisoctahedron.