/// <summary>
        /// Constructor
        /// </summary>
        public Cube3D()
        {
            // initialize cube object
            FullCube = new Cube();

            MovableFaceArray = new BlockFace3D[Cube.MovableFaces];
            for (int BlockNo = 0; BlockNo < Cube.BlocksPerCube; BlockNo++)
            {
                // create block
                Block3D Block = new Block3D(BlockNo);

                // add box to Cube3D VisualMedia3D
                Children.Add(Block);

                // center block (block no 13)
                if (Block.BlockFaceArray == null)
                {
                    continue;
                }

                // loop forall 6 faces of each block
                foreach (BlockFace3D Face in Block.BlockFaceArray)
                {
                    // save movable faces array
                    if (Face.FaceNo >= 0 && Face.FaceNo < Cube.MovableFaces)
                    {
                        MovableFaceArray[Face.FaceNo] = Face;
                    }
                }
            }

            // create double index array of all 6 faces and for each face all blocks
            CubeFaceBlockArray = new Block3D[Cube.FaceColors][];

            // loop for all colors
            for (int ColorIndex = 0; ColorIndex < Cube.FaceColors; ColorIndex++)
            {
                // for each color there are 9 blocks
                CubeFaceBlockArray[ColorIndex] = new Block3D[Cube.BlocksPerFace];

                // loop for all blocks of one face color
                for (int BlockIndex = 0; BlockIndex < Cube.BlocksPerFace; BlockIndex++)
                {
                    CubeFaceBlockArray[ColorIndex][BlockIndex] = (Block3D)Children[BlockNoOfOneFace[ColorIndex, BlockIndex]];
                }
            }
            return;
        }
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        /// <summary>
        /// Block face constructor
        /// </summary>
        /// <param name="Block">Parent Block</param>
        /// <param name="FaceNo">Face number</param>
        /// <param name="FaceColor">Initial face color</param>
        public BlockFace3D(Block3D Block, int FaceNo, int FaceColor)
        {
            // save face number
            this.FaceNo = FaceNo;

            // set current color
            CurrentColor = FaceColor;

            // initialize some geometric variables
            Point3D  Point0 = new Point3D();
            Point3D  Point1 = new Point3D();
            Point3D  Point2 = new Point3D();
            Point3D  Point3 = new Point3D();
            Vector3D Normal = new Vector3D();

            switch (FaceColor)
            {
            case Cube.WhiteFace:
                Point0 = new Point3D(Block.OrigX, Block.OrigY, Block.OrigZ);
                Point1 = new Point3D(Block.OrigX, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ);
                Point2 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ);
                Point3 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY, Block.OrigZ);
                Normal = new Vector3D(0, 0, -1);
                break;

            case Cube.BlueFace:
                Point0 = new Point3D(Block.OrigX, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ + Cube3D.BlockWidth);
                Point1 = new Point3D(Block.OrigX, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ);
                Point2 = new Point3D(Block.OrigX, Block.OrigY, Block.OrigZ);
                Point3 = new Point3D(Block.OrigX, Block.OrigY, Block.OrigZ + Cube3D.BlockWidth);
                Normal = new Vector3D(-1, 0, 0);
                break;

            case Cube.RedFace:
                Point0 = new Point3D(Block.OrigX, Block.OrigY, Block.OrigZ + Cube3D.BlockWidth);
                Point1 = new Point3D(Block.OrigX, Block.OrigY, Block.OrigZ);
                Point2 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY, Block.OrigZ);
                Point3 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY, Block.OrigZ + Cube3D.BlockWidth);
                Normal = new Vector3D(0, -1, 0);
                break;

            case Cube.GreenFace:
                Point0 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY, Block.OrigZ + Cube3D.BlockWidth);
                Point1 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY, Block.OrigZ);
                Point2 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ);
                Point3 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ + Cube3D.BlockWidth);
                Normal = new Vector3D(1, 0, 0);
                break;

            case Cube.OrangeFace:
                Point0 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ + Cube3D.BlockWidth);
                Point1 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ);
                Point2 = new Point3D(Block.OrigX, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ);
                Point3 = new Point3D(Block.OrigX, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ + Cube3D.BlockWidth);
                Normal = new Vector3D(0, 1, 0);
                break;

            case Cube.YellowFace:
                Point0 = new Point3D(Block.OrigX, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ + Cube3D.BlockWidth);
                Point1 = new Point3D(Block.OrigX, Block.OrigY, Block.OrigZ + Cube3D.BlockWidth);
                Point2 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY, Block.OrigZ + Cube3D.BlockWidth);
                Point3 = new Point3D(Block.OrigX + Cube3D.BlockWidth, Block.OrigY + Cube3D.BlockWidth, Block.OrigZ + Cube3D.BlockWidth);
                Normal = new Vector3D(0, 0, 1);
                break;
            }

            // hidden black faces
            if (FaceNo < 0)
            {
                DiffuseMaterial BlackMaterial = new DiffuseMaterial(Brushes.Black);
                Block.Children.Add(CreateTriangle(Point0, Point1, Point2, Normal, BlackMaterial));
                Block.Children.Add(CreateTriangle(Point0, Point2, Point3, Normal, BlackMaterial));
                return;
            }

            // calculate points to separate block edge and block face
            Vector3D Diag02 = Point3D.Subtract(Point2, Point0);
            Point3D  Point4 = Point3D.Add(Point0, Vector3D.Multiply(0.04, Diag02));
            Point3D  Point6 = Point3D.Add(Point0, Vector3D.Multiply(0.96, Diag02));

            Vector3D Diag13 = Point3D.Subtract(Point3, Point1);
            Point3D  Point5 = Point3D.Add(Point1, Vector3D.Multiply(0.04, Diag13));
            Point3D  Point7 = Point3D.Add(Point1, Vector3D.Multiply(0.96, Diag13));

            // gray edge
            DiffuseMaterial GrayMaterial = new DiffuseMaterial(Brushes.DarkGray);

            Block.Children.Add(CreateTriangle(Point0, Point1, Point5, Normal, GrayMaterial));
            Block.Children.Add(CreateTriangle(Point0, Point5, Point4, Normal, GrayMaterial));

            Block.Children.Add(CreateTriangle(Point1, Point2, Point6, Normal, GrayMaterial));
            Block.Children.Add(CreateTriangle(Point1, Point6, Point5, Normal, GrayMaterial));

            Block.Children.Add(CreateTriangle(Point2, Point3, Point7, Normal, GrayMaterial));
            Block.Children.Add(CreateTriangle(Point2, Point7, Point6, Normal, GrayMaterial));

            Block.Children.Add(CreateTriangle(Point3, Point0, Point4, Normal, GrayMaterial));
            Block.Children.Add(CreateTriangle(Point3, Point4, Point7, Normal, GrayMaterial));

            // block face color
            DiffuseMaterial ColorMaterial = Cube3D.Material[FaceColor];

            Block.Children.Add(CreateTriangle(Point4, Point5, Point6, Normal, ColorMaterial, 1));
            Block.Children.Add(CreateTriangle(Point4, Point6, Point7, Normal, ColorMaterial, 2));
            return;
        }