A rhombus with right angles is a square

My wife is a middle school math teacher.  The other night, she asked me if I knew the difference between a rhombus and a square.  Unfortunately, my memory of high school geometry is not so good.  I ended up looking it up on the Internet, because I was curious (I can spare watching reruns of The Office every once in a while!).  Apparently, a rhombus is any four-sided figure (a quadrilateral) with both pairs of opposite sides parallel and all sides the same length, i.e. an equilateral parallelogram!  

Here is the whole classification scheme for quadrilaterals:

Apparently, a rhombus with right angles is called a square!   I completely forgot that one, but then again I haven't had the opportunity to ever use that tidbit of information in my professional life (see the post on my "table of marbles" analogy).  I know what you are thinking right now - what, if anything, does all of this have to do with leadership?  Bear with me a second.  

There are a lot of articles in the management literature on the different leadership archetypes (according to the Harvard Business Review, there are eight archetypes) and styles (I've seen anywhere from three to six different styles described in the literature).  And, while I've written a number of posts in the past about these different leadership styles (see, for example, "Don't be a jerk" and "What style of leadership works best?"), I am still left pondering whether these differences have any significant real world applications.  As I mentioned in one of my previous posts, different situations call for different styles of leadership, and the best leaders often flex back and forth between the different styles depending upon the task at hand.  

Whether you call yourself a democratic leader, an autocratic leader, or a laissez-faire leader, or whether you are a servant leader or a traditional leader, it probably doesn't really matter on a day-to-day basis.  What matters is that you can apply the kind of leadership that is needed in a specific situation.  The different styles and archetypes are important to understand, but collectively they all describe leadership. Democratic leaders, autocratic leaders, or laissez-faire leaders are all leaders.  Just like a rhombus with right angles is a square.