Toy construction system having a variable angle joint

A toy construction system, comprising:

• a member having a number of female twist-lock connectors formed in a surface thereof;
• a number of socket connectors each having a tulip-shaped female socket made of a plastic material having a memory characteristic, each having a socket connector shaft having a mating thread for reversible receipt by one of said female twist-lock connectors,
• said socket connectors having at least three leaves with a space between each adjacent leaf;
• a number of ball connectors, each having a ball connector shaft having a mating thread for receipt by one of said female twist-lock connectors, and each of said ball connectors being of a size for reversible receipt by a socket connector, said ball connector shaft having at least a portion having a diameter adapted to fit into said space, said space allowing for reversibly locking said ball connector shaft at an angle with respect to said socket connector shaft;
• a plurality of said number of female twist-lock connectors having a connector hole with a central core, said connector hole having a groove adapted to receive said mating thread of a socket connector shaft or of a ball connector shaft;
• a plurality of said socket connector shafts and of said ball connector shafts having an opening and an internal passage configured to reversibly receive at least a portion of said central core.