  We study the symmetrised rank-one convex hull of monoclinic-I martensite (a
twelve-variant material) in the context of geometrically-linear elasticity. We
construct sets of T3s, which are (non-trivial) symmetrised rank-one convex
hulls of three-tuples of pairwise incompatible strains. Moreover we construct a
five-dimensional continuum of T3s and show that its intersection with the
boundary of the symmetrised rank-one convex hull is four-dimensional. We also
show that there is another kind of monoclinic-I martensite with qualitatively
different semi-convex hulls which, so far as we know, has not been
experimentally observed.
  Our strategy is to combine understanding of the algebraic structure of
symmetrised rank-one convex cones with knowledge of the faceting structure of
the convex polytope formed by the strains.
