This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

• Lexulous
• Wordscraper
• Wordosaur

n. The state or quality of being symmetrical.

n. (mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane

"It gives the whole thing a nice, what do you call it, symmetricalness."

spatiality    spatial property   

radial symmetry    bilaterality    bilateralism    bilateral symmetry    regularity