  We study snapping and shaky polyhedra which consist of antiprismatic
skeletons covered by polyhedral belts composed of triangular faces only. In
detail, we generalize Wunderlich's trisymmetric sandglass polyhedron in analogy
to the generalizsation of the Jessen orthogonal icosahedron to Milka's extreme
birosette structures, with the additional feature that the belt is developable
into the plane as the Kresling pattern. Within the resulting 2-dimensional
family of origami-like sandglasses we study the 1-parametric sets of
quasi-mechanisms which are either shaky or have an extremal snap, i.e. one
realization is on the boundary of self-intersection. Moreover, we evaluate the
capability of these snapping/shaky quasi-mechanisms to flex on base of the
snappability index and the novel shakeability index, respectively.
