  Photonic crystal topological insulators host protected states at their edges.
In the band structure these edge states appear as continuous bands crossing the
photonic band gap. They allow light to propagate unidirectionally and without
scattering. In practice it is essential to make devices relying on these
effects as miniature as possible. Here we study all-dielectric photonic
topological insulator particles (finite crystals) which do not require a
magnetic field. In such particles the edge states' frequencies are discrete.
Nevertheless, the discrete states support pseudospin-dependent unidirectional
propagation. They allow light to bend around sharp corners similarly to the
continuous edge states and act as topologically protected whispering gallery
modes which can store and filter light as well as manipulate its angular
momentum. In addition, they explain multiple experimental observations of
discrete transmission peaks in photonic topological insulators.
