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