Both of the quilt layouts shown below feature the blocks set on the diagonal -- but with very different results.

The quilt layout featured on the left uses full blocks as well as plain blank blocks (a perfect spot to showcase your quilting design). The additional half blocks form a sort of border around the edges.

The quilt layout illustrated on the right separates the blocks with sashing strips with "cornerstones" to give an added design element to the quilt.

More "Irish" quilt blocks
~ Connemara
~ Danny Boy
~ Irish Puzzle
~ Lucky Clover