The generalization of a tetrahedral region of space to -D. The boundary of a -simplex has 0-faces (Vertices), 1-faces (Edges), and -faces, where is a Binomial Coefficient.

The simplex in 4-D is a regular Tetrahedron in which a point along the fourth dimension through the center of is chosen so that . The 4-D simplex has Schläfli Symbol .

Simplex | |

0 | Point |

1 | Line Segment |

2 | Equilateral Triangular Plane Region |

3 | Tetrahedral Region |

4 | 4-simplex |

The regular simplex in -D with is denoted and has Schläfli Symbol .

**References**

Eppstein, D. ``Triangles and Simplices.'' http://www.ics.uci.edu/~eppstein/junkyard/triangulation.html.

© 1996-9

1999-05-26