Mini Hexchess is an adaptation of the larger 91-cell "Hexagonal Chess" game by the same designer. (The designer notes that, although developed independently, the rules to his larger game are very similar to Glinski's Hexagonal Chess.) The mini game was created in response to a challenge posted on ChessVariants.com.
The game plays like orthodox chess, except the usual moves are interpreted as follows: Orthogonal moves cross hex edges. Diagonal moves follow hex corners, "jumping" over the connecting edges -- moving through spaces of the same color.
Unlike orthodox chess, this game has no castling, no pawn double-move, nor a corresponding en passant capture. This mini game has no queen, so a pawn is not allowed to promote to one.
Each player begins with 5 pawns, a king, a knight, a bishop, and a rook.