Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In ten-dimensional geometry, a rectified 10-simplex is a convex uniform 10-polytope, being a rectification of the regular 10-simplex. These polytopes are part of a family of 527 uniform 10-polytopes with A10 symmetry. There are unique 5 degrees of rectifications including the zeroth, the 10-simplex itself. Vertices of the rectified 10-simplex are located at the edge-centers of the 10-simplex. Vertices of the birectified 10-simplex are located in the triangular face centers of the 10-simplex. Vertices of the trirectified 10-simplex are located in the tetrahedral cell centers of the 10-simplex. Vertices of the quadrirectified 10-simplex are located in the 5-cell centers of the 10-simplex.