With Solomon Golomb's coinage of the term polyomino, puzzlers all over the world have been fascinated with generalizing polygons connected to each other, making rectangles and other forms using only one of each possible piece. This passion of using every usable combination of pieces is shared as well by game designers. Both games and puzzles can settle with just part of the full set of pieces to create the final product, the want to invite every piece to the party is a modest goal that requires some openness to pull off.
Polyform combinations are a good start for this, only needing shapes to be connected to other shapes before racking brains as to how this makes a good game. Instead of polyform pieces, what about basing a game on unit pieces connected into polyforms?
George Sicherman's Moon and Sixpence is a game that deals with this matter. Cards show one of each 6-polyhex, or hexahex, along with a few wildcards. The board is a hexagonal grid for placing coins or stones, if you have any other hexagonal grid board you can also use them for a different experience.
Each players gets dealt six cards, then a card sets the first shape on the board. In their turn, either play their cards or discard a card. If you play a card, you must move a stone to match the shape on the card played whatever the orientation. You can continue to play cards until you can no longer do so, then you draw cards to bring your hand back to six.
Shape cards show the possible orientations and the points it scores if played. Moon cards are wild, letting you move any one stone into any shape but at the cost of two points.
Game ends after every card has been drawn then played or discarded. The player with the most points in played cards wins.
Feel free to add any variations, the game needs them so bad, as it focuses more on the mechanisms of cell-shifting. Although playable, the game can take a while to complete.
Pattern recognition is a must lest you miss out on using a card in a sequence of moves. Being able to play more cards than usual is key as that means more points and more cards to add to your points.
As is, Moon and Sixpence is a decently playable game that is rather straightforward and lacks surprises that a different game of such nature can have. Conceptually base, it lays a basis for games based on the properties of polyominoes that isn't just tile-laying.
