Brother of Trophonius. Agamedes and Trophonius were architects; they designed and built the Temple of Apollo at Delphi and the treasury of King Hyrieus. However, they designed the treasury so that they could remove one stone and have access to the king's wealth. Hyrieus, noticing his diminishing funds, set a trap in order to catch the thief, and Agamedes was caught. Trophonius, worried that he would be implicated, cut off Agamedes' head before he could name his brother as an accomplice.
E2 Dictionary of Classical Mythology