| K12 and the genus-6 tiffany lamp (2004) | |||||||||||||||
Abstract | |||||||||||||||
| The complete graph with 12 nodes, K12, is mapped crossing-free onto a genus-6 surface with the highest degree of symmetry possible. The 66 edges of the graph partition this 2-manifold into 44 three-sided regions, which may then be colored differently. If this shape is illuminated from within, assuming translucent facets, the rendering of a genus-6 “Tiffany Lamp ” can be obtained. A corresponding development can turn K4,4,4, the dual of Dyck’s graph, with 12 nodes and 48 edges, into a highly symmetrical genus-3 “Tiffany Lamp”. | |||||||||||||||
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