Corrections to table in Dr. Math article, http://mathforum.org/library/drmath/view/57699.html. Ray Chandler, rayjchandler(AT)sbcglobal.net, May 10, 2011. Corrections are denoted by *. I split the 1x1 column into two parts to better show the pattern. Column 1x1a counts the rhombi of types 2 and 3 described below; 1x1b counts those of type 1, which fits the pattern of the following columns. Size of rhombus in cm 1x1a 1x1b 2x2 3x3 4x4 5x5 Total 1 by 1 cm 1 1 0 0 0 0 1 2 by 2 4 4 1 0 0 0 9 3 by 3 12 9 4 1 0 0 26 4 by 4 24 16 9* 4 1 0 54* 5 by 5 40 25 16* 9 4 1 95* ____________ /\ /\ / / \ / \ / /____\/____\/ /\ /\ / / \ / \ / /____\/____\/ Here is a rough diagram of the rhombus type we are investigating. This is a 2x2 rhombus and as you can see it is divided into equilateral triangles as opposed to just smaller 1x1 rhombi. If you draw it out on paper more accurately with the diagonals going directly into the corner you will easily see 9 rhombi. We have investigated this type of rhombus and we know there are three types of rhombi to be found within these rhombi. They are roughly drawn below. _ __ /_/ /\ \_\ \/ The first rhombus would have a diagonal running from top left to bottom right, the second has a horizontal line splitting it into 2 equilateral triangles, and the third has a diagonal line running from top right to bottom left.