The Nechushtan graph, illustrated above, is a 10-vertex 5-chromatic graph that is unit-distance in 3 dimensions. It was used by Nechushtan (2002) in the construction of a 6-chromatic graph in 3 dimensions.
The Nechushtan graph is implemented in the Wolfram Language as GraphData["NechushtanGraph"].
The Nechushtan graph 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 Nechushtan graph is illustrated above in several 2-dimensional embeddings.
."
Geombinatorics 30, 5-13, 2020.de Grey, A. and Haugstrup,
A. "Two Small 6-Chromatic Unit-Distance Graphs in 
." Geombinatorics 31, 110-115, 2022.House
of Graphs. "Nechushtan Graph."