The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron.
It is also called the 5-cell, since it consists of five vertices, or pentachoron.
The pentatope is the four-dimensional simplex, and can
be viewed as a regular tetrahedron in which a point along the fourth dimension through the center of is chosen so that . The pentatope has Schläfli
The pentatope is self-dual, has five three-dimensional facets (each the shape of a tetrahedron), 10 ridges (faces), 10 edges, and
five vertices. In the above figure, the pentatope is shown projected onto one of
the four mutually perpendicular three-spaces within the four-space obtained by dropping
one of the four vertex components (R. Towle).