This is an octahedron which has had short pyramids excavated from each of its faces. If the pyramids are made taller, their vertices coincide at the octahedron’s center. At that point, unlike in the figure above, the polyhedron’s volume reaches zero — turning it into a special type of polyhedron called a nulloid:

You may click on this second picture to enlarge it, if you wish.

Software credit: I made these images using Stella 4d, which you can find at http://www.software3d.com/Stella.php.