The term rectification is sometimes used to refer to the determination of the length of a curve.
Rectification also refers to the operation which converts the midpoints of the edges of a regular polyhedron to the vertices of the related "rectified" polyhedron. Rectified forms are bounded by a combination of rectified cells and vertex figures. Therefore, a rectified polychoron is bounded by s and s. For example, is bounded by 600 truncated tetrahedra (truncated cells) and 120 icosahedra (vertex figures). A rectified polyhedron is indicated by prepending an "r" to the Schläfli symbol.
polyhedron | Schläfli symbol | rectified polyhedron | Schläfli symbol |
tetrahedron | octahedron | ||
octahedron | cuboctahedron | ||
cube | cuboctahedron | ||
icosahedron | icosidodecahedron | ||
dodecahedron | icosidodecahedron | ||
16-cell | 24-cell |
Rectification of the six regular polychora gives five (not six) new polychora since the rectified 16-cell is the 24-cell .