The Moser spindle is the 7-node unit-distance graph illustrated above (Read and Wilson 1998, p. 187).
A few other (non-unit) drawings of the Moser spindle are illustrated above.
Bondy and Murty (2008, p. 358) call it the Hajós graph, illustrated above, but do not explain the origin of this name or cite a source for this naming usage.
The Moser spindle is a quasi-cubic graph.
The Moser spindle has chromatic number 4 (as does the Golomb graph), meaning the chromatic number of the plane must be at least four, thus establishing a lower bound on the Hadwiger-Nelson problem. After a more than 50-year gap, the first unit-distance graph raising this bound (the de Grey graph with chromatic number 5) was constructed by de Grey (2018).
The Moser spindle is implemented in the Wolfram Language as GraphData["MoserSpindle"].
