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Koch and Fischer’s C(+–Y) can be generated by a pair of nonagons each with three
straight edges. This corresponds to 1/8
of a unit cell and is illustrated, along with
the unit cell. Below: for +–Y, two
nonagons are linked by a tunnel.
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1/8 unit cell of a minimal balance surface
with the same symmetry as P and C(P).
The patch shown has the same topology
of Costa’s (non-periodic) minimal surface.
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A new non-balanced minimal surface generated by reflections: unit cell, and
1/8 unit cell containing six fundamental patches. There exists a wide variety of non-balanced TPMS. Their classification remains an unexplored problem.
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A non-balanced surface: a unit cell of Schoen’s
FRD. Generated by reflections
in the faces of 1/8 of the unit cell,
which contains a patch with
tetrahedral symmetry:
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A ‘double diamond‘ surface. A pair of
surface of constant mean curvature
belonging to the family of surfaces to
which D (zero mean curvature) belongs.
The triply periodic structure is generated
by reflections in the faces of the
rhombic dodecahedron.
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