! As others have said, planting closely gives "quicker" color, but, you will need to divide sooner. You may want to consider just planting your initial ,single rhizome, in the "center" of your "little" triangles, and letting the clumps develop with a little more space. As was stated, for the first year, or two (until the clumps get very large), you could inter plant with annuals, or even gladiolus , to fill in the blank spaces, and give some color later in the year ?