Determination of all misorientations of tetragonal lattices with low multiplicity; connection with Mallard's rule of twinning

Methods to determine the axial ratios of primitive and body-centred tetragonal lattices admitting multiplicities Σ lower than a chosen upper limit are developed and applied to produce lists giving all cases with Σ ≤ 5 and the corresponding twin mirror planes.

On quaternions and octonions: their geometry, arithmetic and symmetry