## Core Concept
The face receives its rich blood supply from branches of the **external carotid artery** and **internal carotid artery**. Specifically, the external carotid artery branches into several arteries that supply the face, including the **facial artery**, **lingual artery**, **occipital artery**, **posterior auricular artery**, **maxillary artery**, and **superficial temporal artery**. The internal carotid artery contributes through its **ophthalmic artery**, which has branches supplying the medial and upper parts of the face.

## Why the Correct Answer is Right
The **occipital artery** primarily supplies the scalp's posterior aspect rather than providing a significant blood supply to the face itself. While it does contribute to the blood supply of the scalp, its distribution is mainly posterior and not considered a primary supplier to the facial structures.

## Why Each Wrong Option is Incorrect
* **Option A:** The **facial artery**, a branch of the external carotid artery, provides a significant blood supply to the face, particularly the anterior parts.
* **Option B:** The **infraorbital artery**, a branch of the maxillary artery (which itself is a branch of the external carotid artery), supplies the lower eyelid, the side of the nose, and the upper lip, contributing to the facial blood supply.
* **Option D:** The **supraorbital artery**, a branch of the ophthalmic artery (which comes from the internal carotid artery), supplies the forehead and scalp, contributing to the facial blood supply.

## Clinical Pearl / High-Yield Fact
A key clinical point is that the face has a rich and complex blood supply, which is why surgical procedures in this area can sometimes be challenging due to the risk of significant bleeding. The anastomotic network between branches of the external and internal carotid arteries ensures a robust supply but also poses challenges for controlling hemorrhage.

## Correct Answer Line
**Correct Answer: C. occipital artery**.