Sierpiński Tetrahedron Graph -- from Wolfram MathWorld
- ️Weisstein, Eric W.
- ️Tue Sep 12 2017
The th-order
Sierpiński tetrahedron graph is the connectivity graph of black triangles in
the
th
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 -Sierpiński
tetrahedron graph has
vertices and
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