Straight from dictionary.com, we have:
"a) a geometrical or other regularity that is possessed by a mathematical object and is characterized by the operations that leave the object invariant: A circle has rotational symmetry and reflection symmetry.
b) a rotation or translation of a plane figure that leaves the figure unchanged although its position may be altered."
Symmetry on C&C mapping is a resource used by Electronic Arts and several mappers to make a map be perfectly ballanced. The distance between the starting locations and tiberium, choke points, tech buildings, cities, among other map resources will be the same for any starting location of the map. Perfectly ballanced maps allows tournament players to play the map starting on any position with no disadvantages between the players. The latest World Builder comes with a copy and paste tool to make this kind of map easier to be done.
While this may look interesting for online players who plays tournaments, for normals players, these maps are a tragedy. Scouting half or a quarter of the map is enough to have the knowledge of the whole map, making the map predictable during the gameplay (even on C&C3's case where the map already starts revealed with fog), since most players will have the in their mind the whole shape of the map, all possible tech building locations, tiberium patches where the enemy can gather and other strategical positions of the map without sending a single light infantry squad to the enemy or taking their time to analyse the enemy location. Predictable games become repetitive easily, specially when playing against AI.
The symmetry featured was abused by EA in the latest game, due to their RTS As Sport plans. From all maps that came with the original map and Kane Edition, only one map does not contain any symmetry. From the other maps, only one of the maps is almost symmetrical (see the final notes). The other maps are symmetrical. Patch 1.05 included few non symmetrical maps, but the number of non symmetrical maps in the game is still very low. For this reason, we are not accepting symmetrical maps in this contest. We want to make sure the C&C3 Kane's Wrath comes with at least 3 new great non-symmetrical maps and you can make it happen by submitting your best non-symmetrical maps.
The following kind of symmetries are not accepted by us:
-> Tech Buildings
-> Starting Locations
---> 1 vs 1 Oposite Sides
---> Four Sides
---> Four Corners
---> Circular Ring
In order to prevent any confusion with these starting locations symmetry, we've got a quick reference that may help you to understand what are each of these types of symmetry.
1 vs 1 Oposite Sides:
As the name says, players starts exactly in the oposite side of the map:
The players starts exactly in the center of each side of the map:
As the name says, players starts exactly in the four corners of the map. Definitelly the worse of the symmetries for 4 players:
The player starting locations forms a kind of a circle:
Some maps like the one below would bypass our symmetry limitation, although the one below wouldn't do well on the concept category and gameplay for being a very obvious kind of map, however, the starting locations and tiberium positions are not totally symmetrical.