His earlier papers were mostly concerned with crystallography, and the reputation they gained him led to his appointment as Privatdozent at Konigsberg, where in 1828 he became extraordinary, and in 1829 ordinary, professor of mineralogy and physics.
The development of the theory of crystal structure, and the fundamental principles on which is based the classification of crystal forms, are treated in the article Crystallography; in the same place will be found an account of the doctrine of isomorphism, polymorphism and morphotropy.
In the article Crystallography the nature and behaviour of twinned crystals receives full treatment; here it is sufficient to say that when the planes and axes of twinning are planes and axes of symmetry, a twin would exhibit higher symmetry (but remain in the same crystal system) than the primary crystal; and, also, if a crystal approximates in its axial constants to 'a higher system, mimetic twinning would increase the approximation, and the crystal would be pseudo-symmetric.
A point which divides a line, or a line which divides an angle, into two equal parts; in crystallography it denotes the bisector of the angle between the optic axes.
The mensuration of the cube, and its relations to other geometrical solids are treated in the article Polyhedron; in the same article are treated the Archimedean solids, the truncated and snubcube; reference should be made to the article Crystallography for its significance as a crystal form.
Bevelment, as a term of crystallography, means the replacement of an edge of a crystal by two planes equally inclined to the adjacent planes.
In crystallography as " twins."
In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the "pentagonal dodecahedron" of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones.
Hemihedral forms are of special importance in crystallography, to which article the reader is referred for a fuller explanation of these and other modifications of polyhedra (tetartohedral, enantiotropic, &c.).
(Reference should be made to the article Crystallography for illustrations, and for applications of these phenomena to the determination of crystal form.) With an uniaxal plate perpendicular to the optic axis, the curves of constant retardation are concentric circles and the lines of like polarization are the radii: thus with polarizer and analyser regulated for extinction, the pattern consists of a series of bright and dark circles interrupted by a black cross with its arms parallel to the planes of polarization and analysation.
In geometry, and in geometrical crystallography, the term denotes a line which serves to aid the orientation of a figure.