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.
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- Small Cubicuboctahedron
- Small Ditrigonal Dodecacronic Hexecontahedron
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- Small Ditrigonal Icosidodecahedron
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