Hi Mi Ki

From BoardGameGeek:

Hi Mi Ki is a game picturing a showdown between Japanese elementalists, Yamabushis. The game relies on a cube (not dice) tipping mechanic. Each cube figures Water, Fire and Wood on its faces. At your turn you can tip one of your cubes to the next square of the board. This way your cubes change facing as they move on the board. When your cube ends its movement on a square beside an enemy cube there is a confrontation. Water quenches fire, fire burns wood and wood floats on water. If your cube is victorious you take a victory tile. The first player with 6 tiles wins the game. If your cube is on the same side as an adjacent cube you get to play again. The difficulty of the game is to keep track of the always changing cubes on the board. Solo play and 2 vs 2 play are also available in the base game. -description from designer