Math Calligram

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The opposite of the long side is, appropriately, the short side at the
bottom (a->a); but the opposite of the small side at the upper right
is the side just to the left of the bottom (b->b), which seems a lot
less 'opposite'. more examples on help in math,
Does that mean our definition is bad? No, just that
we've defined opposite in terms of counting, and when we deal with
different size sides, that won't match a metric definition. We should
expect a pathological shape to be less intuitive than a "natural"
shape.

Interestingly, your Calligram is by definition one for which two
definitions of 'opposite' agree - not an uncommon way to define a
special kind of object. You sense that 'opposite' ought to mean at
least approximately parallel (as in a circle), so you ask about shapes
that work that way. The problem you've had is an unwillingness to be
inflexible and hold to a topological definition of oppositeness while
you compare it to a Euclidean version; you let the latter leak into
the former while you work, until your definition of a Calligram
becomes so circular that, in the extreme, we could claim that any
polygon with NO parallel sides is a Calligram, because no two sides
are parallel ('opposite'), and therefore all of the opposite sides
(that is, no sides) are parallel. learn more on free math tutoring online.