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 of a 6-chromatic graph in 3 dimensions.
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.
."
Geocombinatorics 30, 5-13, 2020.de Grey, A. and Haugstrup,
A. "Two Small 6-Chromatic Unit-Distance Graphs in 
." Geocombinatorics 31, 110-115, 2022.Nechushtan,
O. "On the Space Chromatic Number." Disc. Math. 256, 499-507,
2002.