  Triangle-hinge models [arXiv:1503.08812] are introduced to describe
worldvolume dynamics of membranes. The Feynman diagrams consist of triangles
glued together along hinges and can be restricted to tetrahedral decompositions
in a large N limit. In this paper, after clarifying that all the tetrahedra
resulting in the original models are orientable, we define a version of
triangle-hinge models that can describe the dynamics of unoriented membranes.
By regarding each triangle as representing a propagation of an open membrane of
disk topology, we introduce a local worldvolume parity transformation which
inverts the orientation of triangle, and define unoriented triangle-hinge
models by gauging the transformation. Unlike two-dimensional cases, this local
transformation generally relates a manifold to a nonmanifold, but still is a
well-defined manipulation among tetrahedral decompositions. We further show
that matter fields can be introduced in the same way as in the original
oriented models. In particular, the models will describe unoriented membranes
in a target spacetime by taking matter fields to be the target space
coordinates.
