Which parameters defines a polar plot? I need to convert a polar plot into a short array of 3-5 values. This array should describe the polar plot as best as possible.

For example, I know that I can use the beamwidth which is also known as the half power. This is the angle between the left and right -3 dB point:



I also know that I can use the the ratio between the surface of the polar plot versus the whole 360° plane. 

Thus, so long I only have two values in the array:


Beamwidth
Ratio polar plot vs plane


But are there other values that can describe the polar plot ? 
And also, how can I have a value which describes second biggest lobe ?
Some examples would be the null to null bandwidth(s) as well as the sidelobe levels of the first/second sidelobes. 

Example vector of 5 numbers:
[mainlobe gain, first null location, 1st sidelobe gain, second null, 2nd sidelobe gain]

From this you could produce an estimate for the 3 dB points of each lobe using some "reasonable" formula, i.e. halfway between the peak and the null.