Complete Graph K7 Embedded on a 3D Torus
thingiverse
K7 is a complete graph featuring 7 vertices, each connected to every other vertex with an edge, resulting in a total of 21 edges. As a non-planar graph, it cannot be drawn on a plane without having some edges intersect. However, it can be embedded onto a torus, allowing all edges to exist without crossing over one another. This design showcases the concept in practice. This object was created by my research student, Zachary Ash, at Grand Valley State University. A companion model illustrating the embedding of the graph on a plane is available online: http://www.thingiverse.com/thing:1625128 The torus depicted in the photograph was printed by Shapeways for approximately $20.
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