The invention herein discloses a system including building blocks intended for educational, amusement or functional use of assembling into mechanical and electro-mechanical constructions. The building blocks are electrically conductive and have an electrical connector with an asymmetry property around one of the main, or natural, assembly planes. The asymmetric properties allow the connector to maintain high electrical conductance when assembled near an adjacent building block, without harming the building blocks physically and without requiring complex assembly rules and restrictions. The system can present rotational symmetry of 180 degrees, and can present elastic properties or magnetic properties to further increase the conductivity and durability of the connectors.