Your squash is ready when the skin has uniform and glossy color and their is a firmness to the rind but you can still dent it easily with your thumbnail. Summer squash is most tender when less than 8 inches long. You can slip a piece of tile or plastic under the squash if it is sitting on the damp earth and this will allow it to keep ripening and not rot where it hits the ground. The mystery squash sounds like a Patty Pan squash with the intersecting shape you describe. Patty pan squash should be light yellow and 4 inches or less in diameter for best harvest. Next year you may also want to try gourd squash that grow in whimsical shapes.