Socket Screws (Cap Screws)
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Socket screws, also known as Allen head screws or bolts, have a hexagonal (hex) internal drive built into the head and are tightened and loosened with an Allen wrench or hex key. They are used in applications where a strong bolt or screw is needed but access is limited. Socket screws are available in standard sizes, custom sizes, or special products manufactured to customer drawings

Socket screws are often recessed below the surface of  the part to reduce danger when part rotate.  Also known as counter boring and counter sinking.