Every point on its surface is equidistant from its centre (6)
I believe the answer is:
sphere
'every point on its surface is equidistant from its centre' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for sphere that I've seen before include "Province - range" , "Ball shape" , "Ball, bubble" , "Ball or field of influence" , "Perfect round" .)