An electronic gaming machine, an electronic gaming system, and a computer-implemented method for providing three dimensional selection games in a gaming system are disclosed. The electronic gaming machines includes: at least one processor; at least one persistent data store; at least one receiver to receive game data for storage in the at least one persistent data store; and a display device configured with a user interface to display: 1) a multi-faceted gaming surface comprising at least two gaming surface representations; and 2) a portion of the game data as a first set of 3D game components on one or more of the at least two gaming surface representations in accordance with a set of game rules for a given game, each one of the 3D game components having a symbol associated thereto.