Final answer:
In patterned brickwork, a brick with a darker end exposed as a header is known as a Flare Header, used to create decorative patterns.
Step-by-step explanation:
In patterned brickwork, the term for a brick with a darker end exposed as a header is called a Flare Header. A flare header is typically a brick that has been fired with one end exposed to higher heat during kilning, which causes that end to become noticeably darker. Such bricks are used intentionally to create decorative patterns in brickwork. For example, a flare header might be incorporated into a design where brick units are laid at an angle to create a sawtooth-pattern frame or used in the construction of corbels that support the roof.