A simplex is the X-dimensional form of the line segment - triangle - tetrahedron series, which is formed by beginning with a point and having the next shape in the sequence be a pyramid with the base of the previous shape. For example, a tetrahedron is a triangle-based pyramid.
The schläfli symbol of an X-simplex is - for example, the schläfli symbol of a pentachoron (4-simplex) is .
All simplices are self-dual.