Tetrix
The 3-D analog of the Sierpinski Sieve illustrated above, also called theSierpinski Sponge or Sierpinski Tetrahedron. Let 
be the number of tetrahedra, 
the length of a side, and 
the fractional Volume of tetrahedra after the
th iteration. Then
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
The Capacity Dimension is therefore
 | |  | |
|  | (4) |
so the tetrix has an Integral Capacity Dimension (albeit one less than the Dimension ofthe 3-D Tetrahedra from which it is built), despite the fact that it is a Fractal.
The following illustration demonstrates how this counterintuitive fact can be true by showing three stages of the rotationof a tetrix, viewed along one of its edges. In the last frame, the tetrix ``looks'' like the 2-D Plane.
References
Dickau, R. M. ``Sierpinski Tetrahedron.''http://forum.swarthmore.edu/advanced/robertd/tetrahedron.html. Eppstein, D. ``Sierpinski Tetrahedra and Other Fractal Sponges.''http://www.ics.uci.edu/~eppstein/junkyard/sierpinski.html.
- Pollard Rho Factorization Method
- Poloidal Field
- Polyabolo
- Polyconic Projection
- Polycube
- Polydisk
- Polygamma Function
- Polygenic Function
- Polygon
- Polygonal Knot
- Polygonal Number
- Polygonal Spiral
- Polygon Circumscribing Constant
- Polygon Construction
- Polygon Division Problem
- Polygon Fractal
- Polygon Inscribing Constant
- Polygon Triangulation
- Polygram
- Polyhedral Formula
- Polyhedral Graph
- Polyhedron
- Polyhedron Coloring
- Polyhedron Compound
- Polyhedron Dissection