Heptagonal Gyroid

The gyroid minimal surface separates two spatial labyrinths of equal volume that wind along two enantiomorphic laves graphs. It can be tiled by heptagons. The embedding of the tilegraph shown here separates spatial labyrinths with the same laves graphs as skeletons, but optimizes for equal length of the heptagonal tiles. Thus the topologies of the separated spaces remain isomorphic in the embedding, while the tiling does not coincide with the gyroid surface.

Interestingly the spirals so characteristic of the chiral laves graph reappear when following subsequences of edge colors formed in the tilegraph.

For more on the gyroid read the still active webpage of Alan H. Schoen.