Leaf "shape" is a particular definitive term in botanical science. There are many shapes of leaves, from conifer needles to kidney- or wedge-shapes to obovate shapes. One classification of leaves that does have only three categories is classification according to veins/nerves. The classification of leaves according to vein or nerve structure specifies the three categories of:
- Pinnate leaves
- Palmate leaves
In parallel-veined leaves, the veins run along-side each other making the leaves very tough and sturdy, as seen in celery stalks or hemp reeds. It's easy to see that the veins in celery stalks run alongside each other throughout the stalk.
In pinnate leaves, nerves are discussed rather than veins. There is a central nerve running up the middle of the leaf from which secondary, smaller nerves branch out to each side.
In palmate leaves, the discussion is again one about nerves rather than veins. In this classification of leaves, there is a central nerve hub from which secondary nerves radiate out as do spokes of a wheel.
When asking about leaf classification that specifies three categories, vein classification is the most common classification with three categories. Otherwise, it is clear that there are many basic blade and edge shapes by which leaves can be classified.