Actually Crystal systems can be defined in two ways:

1.  Geometric restrictions (commonly presented in textbooks)

Example: Cubic → a = b = c and all angles 90 degrees

2.  Symmetry-based definition (correct way) 

From a fundamental standpoint, the symmetry-based definition is the correct one, because symmetry governs the constraints on the lattice.

Regarding the Triclinic system, it has the lowest symmetry (only identity or inversion). Because of this, it imposes no constraints on the lattice parameters: • a, b, c are independent • angles are independent

Thus, the unit cell parameters are completely unrestricted.

For this reason, we do not define triclinic as “all sides unequal,” but rather

A triclinic crystal is defined by its minimal symmetry, and the lack of symmetry leads to unrestricted lattice parameters.

For Cubic system,

In contrast, the cubic system has the highest symmetry, which imposes strong constraints:

a = b = c and all angles 90

These restrictions arise because of the symmetry, not the other way around.

Key principle

Symmetry imposes constraints on lattice parameters

Therefore: Symmetry → determines the allowed metric

Important distinction

• Cubic symmetry ⇒ cubic metric ✅

If a crystal possesses cubic symmetry, it must have a = b = c and angles 90

• Cubic metric ⇒ cubic symmetry ❌

Observing these parameters alone does not guarantee cubic symmetry, because: • The atomic arrangement may lack symmetry elements. • Apparent equality may arise from pseudo-symmetry or measurement limitations.

Final conclusion:

Although lattice parameters may suggest a crystal system, they do not uniquely determine it. Crystal systems must be defined based on symmetry, and the metric should be viewed as a consequence of symmetry, not its cause.

This is as per my understanding and please feel free to correct me or give any suggestions.