And you can even combine your two new words.

'Parallelograms vary. Some have two sets of equal sides, while others have four equal sides.'

Today my new word is پایرهنه.

It means بی کفش و حوراب.

.... با پای برهنه

맨발로

barefoot... shoeless... unshod... discalceated... discalced... 

No, I think better synonyms are:

unfettered, emancipated, uninhibited

It is important that students bring a certain ragamuffin, barefoot irreverence to their studies; they are not here to worship what is known but to question it.

 ~Jacob Bronowski~

The last word I have learnt is lattice.

In mathematics, a lattice is a partially ordered set in which every two elements have a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).

More common, a structure of crossed wooden or metal strips usually arranged to form a diagonal pattern of open spaces between the strips. Used for example in a fence.

As far as I know, both rhombus and rhomboids are parallelograms.  The difference between them is that a rhombus must have 4 sides of equal length and a rhomboid has opposite sides equal.

So, all squares are rectangles, but not all rectangles are squares.

All rhombi (rhombuses) are rhomboids but not all rhomboids are rhombi.

In my 5th grade math classes, we didn't use the term rhomboid.  We used parallelogram exclusively for this. 

The hiearchy of quadrilaterals (Scrutinize this carefully as I am likely to make a mistake.):

quadrilateral, trapezoid, parallelogram, rectangle, rhombus, square

As I said, I believe rhomboid can be substituted for parallelogram. 

But please, if I am wrong, correct me! For the sake of my poor students!!!

That's right. Diamonds might be forever. Diamonds might be a girl's best friend ... but they don't mean much in geometry.