  Special partial matchings (SPMs) are a generalisation of Brenti's special
matchings. Let a \emph{pircon} be a poset in which every non-trivial principal
order ideal is finite and admits an SPM. Thus pircons generalise Marietti's
zircons. We prove that every open interval in a pircon is a PL ball or a PL
sphere. It is then demonstrated that Bruhat orders on certain twisted
identities and quasiparabolic $W$-sets constitute pircons. Together, these
results extend a result of Can, Cherniavsky, and Twelbeck, prove a conjecture
of Hultman, and confirm a claim of Rains and Vazirani.
