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.
de Grey, A. "A Small 6-Chromatic Unit-distance Graph in ."
Geocombinatorics30, 5-13, 2020.de Grey, A. and Haugstrup,
A. "Two Small 6-Chromatic Unit-Distance Graphs in ." Geocombinatorics31, 110-115, 2022.Nechushtan,
O. "On the Space Chromatic Number." Disc. Math.256, 499-507,
2002.