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.
- Spherical Harmonic Closure Relations
- Spherical Harmonic Tensor
- Spherical Helix
- Spherical Point System
- Spherical Polygon
- Spherical Ring
- Spherical Sector
- Spherical Segment
- Spherical Shell
- Spherical Spiral
- Spherical Symmetry
- Spherical Tessellation
- Spherical Triangle
- Spherical Trigonometry
- Spherical Vector Harmonic
- Spheroid
- Spheroidal Harmonic
- Spheroidal Wavefunction
- Sphinx
- Spider and Fly Problem
- Spider Lines
- Spiegeldrieck
- Spieker Center
- Spieker Circle
- Spigot Algorithm