The tetrix is the three-dimensional analog of the Sierpiński sieve illustrated above, also called the Sierpiński sponge or Sierpiński
tetrahedron.
The Wolfram Language as SierpinskiMesh n ,
3].
Let volume of tetrahedra
after the
The capacity dimension is therefore
so the tetrix has an integer capacity dimension (which is one less than the dimension
of the three-dimensional tetrahedra from which it
is built), despite the fact that it is a fractal .
The following illustrations demonstrate how the dimension of the tetrix can be the same as that of the plane by showing three stages of the
rotation of a tetrix, viewed along one of its edges. In the last frame, the tetrix
"looks" like the two-dimensional plane .
See also Chaos Game ,
Menger
Sponge ,
Sierpiński Sieve
Explore with Wolfram|Alpha
References Allanson, B. "The Fractal Tetrahedron" java applet. http://members.ozemail.com.au/~llan/Fractet.html . Borwein,
J. and Bailey, D. "Pascal's Triangle." §2.1 in Mathematics
by Experiment: Plausible Reasoning in the 21st Century. Dickau, R. M. "Sierpinski Tetrahedron."
http://mathforum.org/advanced/robertd/tetrahedron.html . Eppstein,
D. "Sierpinski Tetrahedra and Other Fractal Sponges." http://www.ics.uci.edu/~eppstein/junkyard/sierpinski.html . Kabai,
S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica.
Püspökladány, Hungary: Uniconstant, pp. 159-160, 2002. Kosmulski,
M. "Modulus Origami--Fractals, IFS." http://hektor.umcs.lublin.pl/~mikosmul/origami/fractals.html . Mandelbrot,
B. B. The
Fractal Geometry of Nature. Referenced on Wolfram|Alpha Tetrix
Cite this as:
Weisstein, Eric W. "Tetrix." From MathWorld https://mathworld.wolfram.com/Tetrix.html
Subject classifications
th iteration of the tetrix is implemented
in the Wolfram Language as SierpinskiMesh[n,
3].
be the number of tetrahedra, 
the length of a side, and 
the fractional volume of tetrahedra
after the 
th iteration. Then
