Translation: moves the tile left, right, up, down, or diagonally but neither rotates nor reflects it. The arrows in the example below indicate which directions the tile can move.
The Tile, translated
Rotation: (as the name implies) rotates the tile either 180 or 90 degrees. The circles in the examples below indicate the centers of rotation. The tile can be rotated 180 degrees along its sides.
The Tile, rotated 180 degrees horizontally
The tile can be rotated 180 degrees along its top or bottom.
The Tile, rotated 180 degrees vertically
The tile can be rotated 180 degrees along all sides.
The Tile, rotated 180 degrees horizontally and vertically
The tile can be rotated in 90-degree increments around one of its corners.
The Tile, rotated in 90-degree increments
Reflection: (as the name implies) reflects the tile along an imaginary mirror. The solid lines in the examples below represent mirrors. The tile can be reflected along its sides.
The Tile, reflected horizontally
The tile can be reflected along its top or bottom.
The Tile, reflected vertically
The tile can be reflected along all sides.
The Tile, reflected horizontally and vertically
Glide Reflection: is a combination of reflection and translation. First, the tile reflects along an imaginary mirror. Then, the tile translates along the same line. The dashed lines in the examples below represent mirror/translation lines. The tile can be reflected along its sides, then translated vertically.
The Tile, glide-reflected horizontally
The tile can be reflected along its top or bottom, then translated horizontally.
The Tile, glide-reflected vertically
The tile can be reflected along all sides, then translated horizontally and vertically.
The Tile, glide-reflected horizontally and vertically
