**Core Concept**
The cranial nerves have distinct somatic motor nuclei that control voluntary movements of the face, head, and neck. These nuclei are located in the brainstem and play a crucial role in controlling the motor functions of the cranial nerves.

**Why the Correct Answer is Right**
The cranial nerve with no somatic motor nucleus is the **Vagus Nerve (CN X)**. This is because the vagus nerve primarily has parasympathetic motor functions, controlling involuntary movements such as digestion, heart rate, and respiration. Unlike other cranial nerves, the vagus nerve does not have a somatic motor nucleus that controls voluntary movements.

**Why Each Wrong Option is Incorrect**
* **Option A:** The **Trigeminal Nerve (CN V)** has a somatic motor nucleus that controls the muscles of mastication (chewing).
* **Option B:** The **Accessory Nerve (CN XI)** has a somatic motor nucleus that controls the sternocleidomastoid and trapezius muscles.
* **Option C:** The **Facial Nerve (CN VII)** has a somatic motor nucleus that controls the muscles of facial expression.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the cranial nerves with somatic motor functions are responsible for controlling voluntary movements, whereas those without somatic motor functions control involuntary movements.

**Correct Answer:** C. Facial Nerve (CN VII)