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Sierpiński Tetrahedron Graph

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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

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References

Broden, J.; Espinosa, M.; Nazareth, N.; and Voth, N. "Knots Inside Fractals." 5 Sep 2024. https://arxiv.org/abs/2409.03639.Hinz, A. M.; Klavžar, S.; and Zemljič, S. S. "A Survey and Classification of Sierpiński-Type Graphs." Disc. Appl. Math. 217, 565-600, 2017.

Cite this as:

Weisstein, Eric W. "Sierpiński Tetrahedron Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SierpinskiTetrahedronGraph.html