Answer
Vincent has a great idea, here’s another similar method from a different approach (which I think has less steps)
Create your shapes (all split up etc.)
Select All (Ctrl/Command+A)
Then add in an stroke outline and bump it up to the desired thickness (I would make it white to better see it).
Now go to Object→Path→Outline Stroke
Then select your group and open up Pathfinder:
Window→Pathfinder (Ctrl/Command+Shift+F9)
Now select Divide
Now select and ungroup everything (Right-click→Ungroup or Ctrl/Cmd+Shift+G)
Now select one of the white spots and then go to Select→Same→Fill Color and delete all of them.
You will now have equally spaced gaps between the shapes.
The distance between the shapes will depend on your stroke thickness.
Attribution
Source : Link , Question Author : Libby , Answer Author : WELZ