Which of the following is NOT a type of crystal system?

The pentagonal system is not recognized as a distinct crystal system in crystallography, which is why it is the correct choice here. In crystallography, crystal systems define the symmetry and arrangement of crystal lattices. The well-established systems include cubic, triclinic, hexagonal, orthorhombic, tetragonal, and rhombohedral.

The cubic system is characterized by three equal axes meeting at right angles, and the triclinic system possesses no axes of symmetry with all sides being different lengths and angles. The hexagonal system is defined by four axes, three of which are equal in length and lie in a plane at 120 degrees to one another, with the fourth axis perpendicular. None of these features apply to a pentagonal system, which lacks the foundational criteria to be classified alongside these recognized systems. Thus, the recognition of only six distinct crystal systems underscores the absence of a pentagonal classification.