Two or three play. Each chooses a different color. The players then take turns placing a triangle of their color into a vacant space. After the first turn, a new triangle must touch at least one previous triangle at at least one point. The game ends when all spaces are occupied.
Each play that completes a quadrilateral on the board scores as many points as the number of triangles in the quadrilateral, subject to these conditions:
Because of the third condition, a quadrilateral can be scored only if it contains an even number of triangles. Here is a picture of the 31 sizes and shapes of scorable quadrilaterals on the board.
The board contains 468 such quadrilaterals.
The highest possible score on a single play in Quadrigon is 2,078 points. Here is the scoring:
Thanks to Jonathan Clark for giving me a Quadrigon set—in fact, two of them.
Last revised 2015-10-01.