Taxonomy of polygons

Question

I've written a tree-like layout to help myself remember which polygons are sub-types of others, because I always get confused. I was just wondering if this is right:

|quadrilateral
    |parallelogram
        |rectangle
            |square
            |oblong
        |rhomboid
        |kite (corrected after rschwieb's answer, a rhombus is a kite)
            |rhombus
                 |square
    |trapezoid(AmE) / trapezium (BrE)
    |trapezium(AmE) / irregular quadrilateral

So a square is a rhombus and a parallelogram.

Also, I know that there are two definitions of "trapezoid." Under the inclusive definition "trapezoid" is immediately under "quadrilateral" in the tree and above parallelogram and kite. Under this definition all squares are trapezoids.

Is my tree correct, at least ignoring the difference in the trapezoid definition difference?

Edit: Thanks to rschwieb for helping me realise that a rhombus is a kite. There is also a nice Euler diagram Wikipedia

Answer 1

Can't a kite also be a parallelogram, in the case where all sides are equal?

That of course depends on your definition of kite... I've rarely seen the term used at all. You can exclude that case specifically and your tree is then okay.

Wikipedia's Kite (geometry) article seems to include that in their special cases.

EDIT: In that special case, it can also be a rhombus or a square

Answer 2

You need to see this post I wrote some time ago.

In short, the education system (at least in the US) has confused this issue and made it harder than it has to be.

There is a very natural hierarchy the depends on logical connections between quadrilaterals, and there is really no benefit to using the “exclusive version” of definitions.

I would argue for this picture for the main characters:

Actually there is a little puzzle where you can figure out a new node to insert between "quadrilateral" and "kite" which also connects to "parallelogram," and I have never seen this shape mentioned in a textbook. It's just not common enough to encounter in normal life.