= Heawood torus map
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Triangulate a <torus> using the seven vertices of the <complete graph> $K_7$ and oriented triangles $(i,i+1,i+3)$ and $(i,i+3,i+2)$, with indices modulo seven. Every edge occurs twice with opposite orientations; each vertex has a cyclic link. The <Euler characteristic> is $7-21+14=0$. Its <dual graph> is the <Heawood graph>. This dual map has seven disc faces, each adjacent to all the others, so it needs seven face colors although its edges have a <Tait coloring>.
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