Sierpiński tetrahedron

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.

Menger sponge graph | Sierpiński gasket graph | tetrix