The Gyroid Triply Periodic Minimal Surface

Alan Schoen's gyroid surface is a triply periodic minimal surface that has no planes of symmetry and no embedded straight lines. It does have C3 axes of symmetry (along one diagonal of the unit cell) and 4-fold roto-inversion axes.

Alan Schoen recently wrote a description of his discovery of the gyroid.

The gyroid is intermediate between the D-surface and the P-surface
in the sense of being a Bonnet rotation of the D-surface by
38.0147739891081 degrees, while the P-surface is a Bonnet
rotation by 90 degrees (play movie). Thus the gyroid is locally isometric to both
the D-surface and the P-surface.

Small metal sculptures of the gyroid are available from Bathsheba Sculpture Bathsheba gyriod

Click on the images for larger versions.

gyroid unit cell A cubic unit cell of the gyroid. Note that the cube faces are not symmetry planes.
gyroid 8 unit cells A piece of gyroid that is two unit cells in each direction. There is a C3 symmetry axis along the cube diagonal from the upper right corner.
gyroid C3 axis Looking along the C3 axis.

Surface Evolver datafiles for the gyroid.
gyroid-cube.fe A cubic unit cell with a coarsely meshed gyroid. Torus model. With squared mean curvature for energy, so it is stable in evolution.
gyroid-hex.fe A hexagonal region of the D surface, with scripts for displaying multiple copies and doing Bonnet rotation. Also contains the scripts for making the movie.
gyroid-tri.fe A triangular fundamental region of the surface. Comes with three view transform generators, one for each edge, so you can play around making your own patches of surface with the transform_expr command.
Some hand-picked sets of transforms of the fundamental region triangle.
15views.fe 42views.fe
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