Learn Farsi: تقارن در لچک‌های این قالیچه بی‌نظیر است. - The symmetry in the corner pieces of this small rug is unique.

The word qâli means carpet or rug. The suffix -che is a common diminutive marker in Farsi that means "small". Therefore, qâliche specifically refers to a small rug.

What exactly does lachak refer to in this context?

In traditional Persian arts and architecture, a lachak is a triangular corner piece. In carpet weaving, it refers specifically to the ornate triangular patterns found in the four inner corners of a rug's central field.

How is the adjective bi-nazir formed?

It combines the prefix bi- (without) and the Arabic loanword nazir (peer, match, or equal). Together, they literally mean "without equal", which is used to mean unique or matchless in Farsi.

Could we use the formal verb 'ebârat ast az' here instead of 'ast' since we are detailing the rug's features?

No, because ebârat ast az means "consists of" or "is defined as" and is strictly used to break down a whole into its components (e.g., if you were listing the materials the rug is made of). This sentence is simply stating that a specific quality (taqâron, or symmetry) is unique (bi-nazir), so the simple copula verb ast (is) must be used.