  Colloidal suspensions have long been studied as a model for atomic and
molecular systems, due to the ability to fluorescently label and individually
track each particle, yielding particle-resolved structural information. This
allows various local order parameters to be probed that are otherwise
inaccessible for a comparable molecular system. For phase transitions such as
crystallisation, appropriate order parameters which emphasise 6-fold symmetry
are a natural choice, but for vitrification the choice of order parameter is
less clear cut. Previous work has highlighted the importance of icosahedral
local structure as the glass transition is approached. However, counting
icosahedra or related motifs is not a continuous order parameter in the same
way as, for example, the bond-orientational order parameters $Q_{6}$ and $W_6$.
In this work we investigate the suitability of using pentagonal bipyramid
membership, a structure which can be assembled into larger, five-fold symmetric
structures, as a finer order parameter to investigate the glass transition. We
explore various structural and dynamic properties and show that this new
approach produces many of the same findings as simple icosahedral membership,
but we also find that large instantaneous displacements are often correlated
with significant changes in pentagonal bipyramid membership, and unlike the
population of defective icosahedra, the pentagonal bypyramid membership and
spindle number do not saturate for any measured volume fraction, but continues
to increase.
