Pseudo Tricubes with Corner Connections

If you connect three cubes at their faces, edges or corners, you get 16 different pieces. Jared McComb asked to add the pieces with corner connections to the existing set of pseudo tricubes, which are only joined at faces or edges. I used triangular antiprisms to do the job. They connect the little triangles at the corners of two cubes. With these pieces you can construct a 4x4x3 box and some other figures.