**Core Concept**
The pterygomandibular space is a fascial space in the infratemporal fossa, located between the lateral pterygoid muscle and the medial surface of the mandible. It is an important anatomical region for surgical procedures, particularly for the extraction of lower wisdom teeth.

**Why the Correct Answer is Right**
The long buccal nerve, which is a branch of the mandibular division of the trigeminal nerve, primarily supplies the buccinator muscle and the skin of the cheek. Unlike the other options listed, it does not pass through the pterygomandibular space. Instead, it enters the buccal fat pad and then courses superficially to supply the overlying skin and mucosa.

**Why Each Wrong Option is Incorrect**
**Option A:** The nerve to mylohyoid, also known as the mylohyoid nerve, is a branch of the inferior alveolar nerve that passes through the pterygomandibular space to supply the mylohyoid muscle and the anterior belly of the digastric muscle.

**Option B:** The chorda tympani is a nerve that passes through the pterygomandibular space, carrying taste fibers from the anterior two-thirds of the tongue and preganglionic parasympathetic fibers to the submandibular ganglion.

**Option D:** The nerve to the medial pterygoid, which is a branch of the main trunk of the mandibular nerve, also passes through the pterygomandibular space to supply the medial pterygoid muscle.

**Clinical Pearl / High-Yield Fact**
The pterygomandibular space is bounded by the lateral pterygoid muscle, the medial surface of the mandible, and the superior constrictor muscle of the pharynx. Knowledge of this space is crucial for surgeons performing lower wisdom tooth extractions to avoid damage to the nerves and vessels that pass through it.

**✓ Correct Answer: C. Long buccal nerve**