Haüy indices are small integers (p, q, r) used to define the orientation of a given crystal face according to Haüy's law.
They are defined by p = OP/a, q = OQ/b and r = OR/c where:
- a, b and c are the lengths of the edges of the primitive parallelepiped, respectively, along the reference axes Ox, Oy and Oz;
- OP, OQ and OR are the lengths intercepted by the crystal face on the reference axes Ox, Oy and Oz.
Haüy's indices were simplified by Miller who inverted the values (giving the Miller indices).
Definition of the Miller indices of a plane. © Christophe Dang Ngoc Chan, Wikipedia CC by sa 3.0