Everything is a polyhedron, even you and me. Just like in geometry there are duals (where each shape has a shape equal and opposing to it) in physics there is matter and antimatter. The theory holds that there is a universe equal to and opposing our own. If you are old enough to remember when photagraphs were made in a darkroom from negatives you may understand this concept. Our universe is a mirror image in negative to our antiuniverse! Another comparison is a cookie shape cut out of dough. The cookie is the matter, the space left in the dough is the antimatter. The "Conseil Européen pour la Recherche Nucléaire" (CERN) which translated to English means European Organization for Nuclear Research has a fun and informative website all about it. See the kids corner to learn about The Mystery of Antimatter or try Antimatter Academy for older "kids". You will be taken on an investigative journey through space and time to understand the very basics of matter and antimatter and how our universe and all within it is created. A word of advice: If on your voyage you happen to come across your own antimatter stay far away! Scientists have proven that matter and it's own dual antimatter annihilate one another.
This and more interesting and exciting information about matter and antimatter can be found on the CERN website.