The Asscher cut diamonds is no different, with the story behind its invention, popularity, decline, and recent re-popularity. Although it is currently one of the most famous diamond cuts. An Asscher shape diamond is an octagonal diamond with a square shape and layered faceted faces. Asscher shape look very similar to emerald cut, the most obvious difference being that they are square as opposed to rectangular. Asscher diamonds are cut with a focus on clarity rather than shine.