  In general a contractible complex need not be collapsible. Moreover, there
exist complexes which are collapsible but even so admit a collapsing sequence
where one "gets stuck", that is one can choose the collapses in such a way that
one arrives at a nontrivial complex which admits no collapsing moves. Here we
examine this phenomenon in the case of a simplex. In particular we characterize
all values of $n$ and $d$ so that the n-simplex may collapse to a d-complex
from which no further collapses are possible. Equivalently and in the language
of high-dimensional generalizations of trees, we construct hypertrees that are
anticollapsible, but not collapsible. Furthermore we examine anticollapsibility
in random simplicial complexes.
