There are six regular convex polytopes in 4D, which are analogous to
the five Platonic solids in 3D. This is the second, analogous to the
octahedron, called the cross polytope.
The cross polytope is dual to the hypercube, so its
16 cells correspond to the 4-cube's 16 corners. This projection is a straightforward Schlegel diagram. A different projection is here.