mathworld.wolfram.com

Sierpiński Tetrahedron Graph -- from Wolfram MathWorld

  • ️Weisstein, Eric W.
  • ️Tue Sep 12 2017
Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld

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

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