public class SpaceShip extends Polygon {

    //x and y coordinates
    public static int[] polyXArray = {...};
    public static int[] polyYArray = {...};

    //other class variables
    {...}

    public SpaceShip() {

        super(polyXArray, polyYArray, polyXArray.length);
    }
}

public abstract class GameShape extends Polygon {

        //x and y coordinates, still unassigned
        public static int[] polyXArray, polyYArray;

        //other class variables
        {...}

        public GameShape() {

            super(polyXArray, polyYArray, polyXArray.length);
        }
}

public abstract class GameShape extends Polygon {

        //x and y coordinates, still unassigned
        public int[] polyXArray, polyYArray;

        //other class variables
        {...}

        public GameShape() {
            instantiatePolyArrays();
            super(polyXArray, polyYArray, polyXArray.length);
        }

        protected abstract void instantiatePolyArrays();
}