  Frank-Kasper (F-K) phases form an important set of large-cell crystalline
structures describing many inter-metallic alloys. They are usually described in
term of their atomic environments, with atoms having $12, 14, 15$ and $16$
neighbours, coded into the canonical $Z_p$ cells (with $p$ the coordination
number), the case $p=12$ corresponding to a local icosahedral environment. In
addition, the long range structure is captured by the geometry of a network
(called either "major skeleton" or "disclination network") connecting only the
non-icosahedral sites (with $p\ne 12$). Another interesting description, valid
for the so-called "layered F-K phases", amounts to give simple rules to
decorate specific periodic 2d tilings made of triangles and squares and
eventually get the 3d periodic F-K phases. Quasicrystalline phases can sometime
be found in the vicinity, in the phase diagram, of the F-K crystalline alloys;
it is therefore of interest to understand if and how the standard F-K
construction rules can be generalized on top of an underlying quasiperiodic
structure. It is in particular natural to investigate how well square-triangle
quasiperiodic tilings with dodecagonal symmetry, made of square and
(equilateral) triangles, can be used as building frames to generate some
F-K-like quasicrystalline structures. We show here how to produce two types of
such structures, which are quasiperiodic in a plane and periodic in the third
direction, and containing (or not) $Z_{16}$ sites.
