The Heawood graph corresponds to the seven-color torus map on 14 nodes illustrated above. The Heawood graph is the point/line Levi graph
on the Fano plane (Royle).
Chvátal (1972) conjectured that point-line incidence graphs of finite projective planes, the smallest example of which is the Heawood graph, were not unit-distance embeddable. The first explicit embedding refuting this conjecture was found by Gerbracht (2008), and exactly 11 such embeddings (illustrated above) were published by Gerbracht (2009) following a general outline first suggested by Harris (2007).
An apparent unit-distance embedding based on a central hexagon has also been constructed by E. Gerbracht (pers. comm., Jan. 2010).
Another unit-distance embedding has apparently been found by Horvat (2009), illustrated above.
The Heawood graph is the second of four graphs depicted on the cover of Harary (1994).
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