Construction
As a unit distance graph, the Moser spindle is formed by two rhombi with 60 and 120 degree angles, so that the sides and short diagonals of the rhombi form equilateral triangles. The two rhombi are placed in the plane, sharing one of their acute-angled vertices, in such a way that the remaining two acute-angled vertices are a unit distance apart from each other. The eleven edges of the graph are the eight rhombus sides, the two short diagonals of the rhombi, and the edge between the unit-distance pair of acute-angled vertices.
The Moser spindle may also be constructed graph-theoretically, without reference to a geometric embedding, using the Hajós construction starting with two complete graphs on four vertices. This construction removes an edge from each complete graph, merges two of the endpoints of the removed edges into a single vertex shared by both cliques, and adds a new edge connecting the remaining two endpoints of the removed edge.
Another way of constructing the Moser spindle is as the complement graph of the graph formed from the utility graph K3,3 by subdividing one of its edges.
Read more about this topic: Moser Spindle
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