There are 2 main types of rectangle. An oblong rectangle is where the height of the rectangle is greater than the width, and obtuse, where the width is greater than the height.
This classification was made by renowned mathmetician Fred Holness is 1972.
An incomplete list of "lesser rectangles" can be found below:

The symbian-hybrid influx rectangle
The hope-peterssen rectangle
The inverse-triangular rectangle
The obtuse-inverse triangle rectangle
The regular-inverse triangle rectangle
The obtuse regular-inverse triangle rectangle
The quimm-hardely rectangle (hypothetical)
The semi-obtuse regular-inverse triangle rectangle (which differs by having curved lines on an axis other than x,y or z)

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