A grid is usually made with the two sets of lines at right angles to each other, creating a lot of little squares. I recently found myself wondering how things would look if, instead of small squares, I began with small diamond shapes. That meant doing a set of parallel lines and doing the second set diagonally.
I thought Knightsbridge would look rather harlequin-y, and I was right. Others I assumed would seem as if I was looking at them on a angle rather than straight on. Right again, Cubine for instance, or Up and Across. I usually do Cubine with an added corner; it makes it look more as if there's a "front".
The top tile uses Bales, Corn Rows (variation by Linda Farmer), Cubine, Facets, Knightsbridge, Up and Across, and Yincut. Facets ended up with 'squashed' gems; I think it would be rather different had I gathered the lines in the acute angles instead of the obtuse ones.
The bottom tile uses Demi, Dex, Flukes, Puf, St. John's Cross, and... yes, umm... 'Nzeppel; I botched the grid and it was too square so I did a random N'zeppl in that section. Like Facets, I think Demi would have quite a different look if I'd divided the diamonds the long way instead of the short way, and Flukes if I'd put the little black bit in the wide corner instead of the tight one.