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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
.
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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
.
See also Complex, Cross Polytope, Equilateral Triangle, Line Segment, Measure Polytope, Nerve, Point, Simplex Method, Tetrahedron
References
Eppstein, D. ``Triangles and Simplices.''
http://www.ics.uci.edu/~eppstein/junkyard/triangulation.html.