Filling spaces without manually using smart fill for combined shapes

I am creating some geometric patters with the transform tool.  Basically a shape is rotated about a center point.  When the shapes are combined they create some quick interesting shapes.  However, is there a way to fill in the gaps in the combined shape automatically, without having to manually use the smart fill tool?  Breaking the shape apart does not help, because the geometric pattern is based on the overlaps.  I included a jpg of what I am doing to circumvent the manual smart fill, but is there an easier way, especially where the geometric patterns become very complex. 

I can take the object, trim from a background, break apart that trimmed shape, then color it, or group or shape into a single curve, then align and group with the original object.  But just looking to see if there is another easier way.