The simplest shape for a corner desk is a triangle with three flat sides, two of which are against walls. There are other options, depending on where you will place the desk. The front edge of a triangle top can curve inward or outward, either for looks or for convenience of use.
The top can also be L-shaped. It may be asymmetrical--longer on one side than the other. The sides of the 'L' may be attached to the main desk, or they may be entirely separate units.
Tops don't have to be flat. An artist's or draftman's table may have a slanted top.
There are two aspects to height--desktop height and unit stand height. The top of the desk can be designed for a standard chair, which means the desktop is about 30 inches above the floor. Or the desktop can accommodate a particular chair or stool. For people who like to work while standing, a top that is waist-high is often a good fit.
The entire unit may be as high as the desktop, commonly seen in wall-mounted desks. It may also come slightly higher than the desktop, incorporating a computer monitor shelf or a small storage unit for pencils, pens and office supplies. At the extreme, the entire unit may reach the ceiling, equipped with several shelves for books or pictures. Such units blur the line between furniture and built-ins.
A corner desk may have no legs at all if the desk is mounted on the wall.
A wall-hung corner desk can be installed using wooden cleats or brackets. Bracket hardware systems each offer unique fittings and storage options.
If the desk has legs, they can be made from iron or plastic pipe, wood, or readymade cabinets. Anything that can support the top can become a "leg."
Shelves are a frequent addition to corner desks, often resembling an étagère with a desktop at the appropriate height. Enclosed cabinets can be incorporated into the design as well. Cabinets can be used as supports for the top. A simple top can be put on legs, with cabinets that can be rolled underneath. Rolling storage is particularly useful for corner desks, where there can be a distance between the front edge of the desk and the corner walls.