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Notes -
The "small" definition isn't that it's a parallelogram with one right angle. For instance, the definition "a polygon with five or fewer sides, parallel sides, and one right angle" seems to be smaller in the sense of having fewer explicit constraints (but of course if it defines the same thing it always has the exact same implicit constraints).
Actually, I am not convinced that "smaller description" is a well defined term at all, unless you're just counting words.
There’s always Kolmogorov complexity. I don’t think it’s terribly helpful for deciding between geometric options—most of the program is going to be the geometric axioms, and then a little will handle drawing lines under those axioms.
Kolomogorov complexity varies with your programming language. If your programming language is "English", the phrase for "rectangle" with the smallest Kolmogorov complexity is "rectangle". If you're not allowed to use the word, the phrase would be something like "equiangular quadrilateral".
If we avoid geometry, consider that the "small" definition for a unicorn is arguably "member of the empty set". I don't need to mention that it has one horn, for the same reason that your definition of "rectangle" doesn't need to mention the other three angles--in fact, I don't need to mention any traits at all.
Of course, you get into the issues in Naming and Necessity, where just because two definitions point to the same set of things doesn't make them interchangeable. "He learned that the morning star is the evening star" is not equivalent to "he learned that the morning star is the morning star", even though the morning star is the same object as the evening. (And no, I'm not namedropping a famous book to look clever; it's one of the few philosophy books I've actually read.)
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