There a three types of tessellations: Translation, Rotation, and Reflection.
Notice how the Scarabs and Owls translate from side to side, as well as, up and down as they repeat.
Student work, "Owls" - 2011
Notice how the Fish and the Queens rotate as they repeat over and over.
Student work "Snooty Queen" - 2011
Notice how the Horsemen and Fish reflect each other as they repeat.