The half square triangle unit is probably the most commonly used patch in a quilt block -- well it is second only to the square. It is made simply with two triangles, filling up half the square each -- hence the name. Take a quick look through this website, or in any quilting magazine, and you will start to notice that this half square triangle, regardless of its size, is present in more quilts than not.
Cat and Mouse
Free Quilt Block Pattern
The Cat and Mouse quilt block is a four patch using half square triangle cut pieces individually rather than as two pieces to make a square. Secondly, this block makes use of the square in the square patch, but again, not in the traditional manner -- but it does require the cutting of the patch as such.
This all sounds very complicated, but the making of this block is relatively simple, so have no fear.
The illustrated sample quilts show how versatile this quilt block is in the resultant quilt that you choose to make.