Sierpiński Tetrahedron Graph

Sierpinski tetrahedron graphs

The nth-order Sierpiński tetrahedron graph is the connectivity graph of black triangles in the nth iteration of the tetrix fractal. The first three iterations are shown above. It is the three-dimensional analog of the Sierpiński gasket graph and can be further generalized to higher dimensions (D. Knuth, pers. comm., May 1, 2022).

The n-Sierpiński tetrahedron graph has 2(4^(n-1)+1) vertices and 6·4^(n-1) edges.

See also

Menger Sponge Graph, Sierpiński Gasket Graph, Tetrix

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Sierpiński Tetrahedron Graph." From MathWorld--A Wolfram Web Resource.