The runcinated tesseract has 16 tetrahedra, 32 cubes, and 32 triangular prisms. Each vertex is shared by 4 cubes, 3 triangular prisms and one tetrahedron.
Read more about Runcinated Tesseract: Runcitruncated Tesseract, Runcitruncated 16-cell, Omnitruncated Tesseract, Related Uniform Polytopes