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# Tritetrahedral Graph

The tritetrahedral graph is the skeleton of the tritetrahedron, a concave polyhedron formed by joining three regular tetrahedra at their faces. It is a 3-tree.

The tritetrahedral graph is the graph square of the A graph, Beineke graph , and 6-matchstick graph 20. If is also the graph cube of the path graph .

The Nechushtan graph, a 10-vertex 5-chromatic graph in 3 dimensions, consists of two copies of the tritetrahedral graph (de Grey and Haugstrup 2022) and is denoted in de Grey (2020) and in de Grey and Haugstrup (2022).

The tritetrahedral graph is implemented in the Wolfram Language as GraphData["TritetrahedralGraph"].

Nechushtan Graph, Tritetrahedron

## Explore with Wolfram|Alpha

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## References

de Grey, A. "A Small 6-Chromatic Unit-distance Graph in ." Geocombinatorics 30, 5-13, 2020.de Grey, A. and Haugstrup, A. "Two Small 6-Chromatic Unit-Distance Graphs in ." Geocombinatorics 31, 110-115, 2022.

## Cite this as:

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