The present invention is an educational and recreational apparatus having a geometrical structure game device comprising a framework of tubes and connector wires characterized by a plurality of nodes on which game pieces can be embedded. Each node comprises a cluster of portions of two or more pairs of connector wires, with the nodes of a game device being identical or differing from one another in the number of pairs of connector wires that form the nodes. The game device can take the form of a two-dimensional or three-dimensional, single-plane or multi-plane, latticed or non-latticed geometrical structure. The game is played with two sets of game pieces, one set for each of two players. The game pieces have slots therein for accommodating the connector wire portions that make up a node, with each set including game pieces that vary according to the variety of nodes in a game device. The game pieces in each group are categorized by different degrees of freedom as determined by the number of slots in the game piece. The game is played by embedding game pieces on the different nodes according to a set of rules, and the player who occupies more nodes than opponent wins the game.