The derivation of the crystal lattice and the assignment of a Bravais lattice type has objective limits.
In general, due to measurement and imaging errors, the approximation of pseudosymmetric lattice types is the rule.
So there is always the danger to consider a higher symmetric lattice as solution.
The first reason for this is that from a purely metrological point of view alone, angles of exactly 90°, for example, will never result. The same applies of course to special ratios between basis vectors.
The second reason is that the symmetry of a crystal structure imposes certain requirements on the metric of the crystal lattice, but crystal symmetry cannot be inferred from the crystal lattice metric.
Unfortunately, in the past years, mostly due to carelessness, description errors of crystal lattices have crept in [1].
For example, for orthorhombic lattices is assumed that a, b and c must be different, but actually no conditions at all are put to the lengths [2]. This means that also for an orthorhombic phase a = b = c can occur.
The following table shows that up to orthorhombic no conditions are defined for the length ratios of the basis vectors.
Definition of the conditions for lattice parameter ratios and angles of different translation lattice .
Once derived lattice parameters plus agreed uncertainties describe a high-symmetric lattice, it is not clear whether the remaining deviations are due to measurement or imaging errors or really exist, i.e. the lattice is possibly not so high-symmetric but described by one of the other solution presented.
But again: Even with practically non-existing deviations it follows that e.g. a phase with cubic lattice metric does not necessarily have cubic symmetry. It is merely very probable.
Therefore, CALM always lists a triclinic lattice description (aP), but additionally also possible higher-symmetric solutions.
[1] Nespolo, M.: The ash heap of crystallography: restoring forgotten basic knowledge. J. Appl. Cryst., 2015, 48, 1290-1298
[2] Hahn, T,: International Tables for Crystallography, Vol.A (2005), 5th ed., Springer,Table 3.1.2.1, p.44