Rectified Tesseract

This is a model of a projection of a uniform four dimensional object, called the rectified tesseract. The tesseract is a four dimensional hypercube, consisting of eight cubes. In the rectified version all vertices are cut off so all cubes becomes cuboctahedra and the vertices itself (where 4 cubes joined) are turned into tetrahedra.

In this particular projection to the 3rd dimension, the volume in which the object is projected is parallel to the cuboctahedra that are closest and furthest away. As a result these aren't deformed in the projection and therefore the cuboctahedron on the outside and the one most on the inside aren't deformed of the projection and they are still real cuboctahedra.