A notation Ludwig Schläfli introduced to help classify the regular polytopes. The Schläfli symbols for the five Platonic solids are {3,3} tetrahedron, {4,3} cube, {3,4} octahedron, {5,3} dodecahedron, and {3,5} icosahedron. The symbol {p,q} represents that faces are p-gons, q of which meet at each vertex.

In four dimensions, the symbol {p,q,r} represents that there are r 3-dimensional faces about each edge that are polyhedra with symbol {p,q}. The 4-dimensional regular polytopes are {3,3,3} pentatope, {3,3,4} orthoplex, {4,3,3} tesseract, {3,4,3} octaplex, {5,3,3} dodecaplex, and {3,3,5} tetraplex. Here the tesseract and pentatope are the 4-dimensional hypercube and simplex respectively; in n dimensions, the hypercube and simplex have symbols {4,3,3,…,3} and {3,3,…,3}.