Fluorite is calcium fluoride, and it is the reference point for 4 on the Mohs scale — which is the single most useful fact about it, because a steel knife cuts it easily and that separates it from almost everything it is mistaken for. Purple fluorite gets sold as amethyst, green fluorite as emerald, and both fail a knife test in one second.
Its second signature is cleavage. Fluorite cleaves perfectly in four directions, along the faces of an octahedron, which means a broken piece shows flat triangular mirror faces and a struck cube tends to lose its corners in neat octahedral chips. Nothing in the quartz family does this — quartz has no cleavage at all.
The third is the property that carries its name. Fluorite fluoresces under ultraviolet light, usually a strong blue-violet, and the phenomenon was named after the mineral rather than the other way round. A cheap UV torch makes this an instant and rather satisfying confirmation.