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.
Free Quilt Block Pattern
The Diamond Star quilt block can only be named as such (at least in my opinion) because it has squares set on point, looking like 'diamonds'. There are actually no diamond patches in this quilt block and so, as a result, it is much easier in the construction process. (Diamond patches tend to get over-handled resulting in distorted pieces). So the fact that there are no diamond patches is a good thing!
This block is fun to make, and gives a little variation on the usual 'star' quilt blocks. There are both large and small pieces so it is an enjoyable process to make the final product.