Simplex
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 throughthe 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.
- Hardy-Littlewood Tauberian Theorem
- Hardy-Ramanujan Number
- Hardy-Ramanujan Theorem
- Hardy's Inequality
- Hardy's Rule
- Harmonic Addition Theorem
- Harmonic Analysis
- Harmonic Brick
- Harmonic Conjugate Function
- Harmonic Conjugate Points
- Harmonic Coordinates
- Harmonic Decomposition
- Harmonic Divisor Number
- Harmonic Equation
- Harmonic Function
- Harmonic-Geometric Mean
- Harmonic Homology
- Harmonic Logarithm
- Harmonic Map
- Harmonic Mean
- Harmonic Mean Index
- Harmonic Number
- Harmonic Progression
- Harmonic Range
- Harmonic Ratio