Abstract: A construction system where elements have connection components for a ball-to-socket or socket-to-socket connection. The ball-to-socket connection "locks" at orientations when one or more detents in the interior of the socket protrude into one or more of a plurality of dimples on the ball. The construction elements generally have an elongated body with a dimpled ball at one end and a socket at the other end, or dimpled balls at both ends, or sockets at both ends. In addition to the ball-and-socket connection, elements may connect in a socket-to-body connection, or a number of different types of socket-to-socket connections. The socket has at least two petals with a lip contour such that in one type of socket-to-socket connection the pair of sockets interlock to form a sphere. The irregular shape of the lip of the socket allows a ball to be leveraged out of a socket, and make orientations over at least 2.pi. steradians available in a ball-to-socket interconnection.