I would strongly suggest that anyone building this stool project consider mounting only a round seat plate to finish this project. It will be worth the extra time used in setting the circle to mark for the template. Also, by adding wood surfaces sandwiching the top as well as below the seat (even if pieces below are in sections), mounted by drilling 1/4" bolt holes and countersinking the top side holes for stove bolts for a flush surface, the builder can use hard foam glued in place and shaped with an electric carving knife. This can then be covered with a small amount of upholstery material and stapled with 1/2" - 3/4" staples suitable for use in wood. A plain steel seat top can be brutal in cold weather. You can even sculpt the hard foam in the shape of a motorcycle solo "bike" seat to decrease pressure on the backs of your thighs. The amount of covering is so small you may get a piece free from scraps at your local upholsterer.

But, by all means, try your best to use a round top to avoid the inevitable injury from running into those corners - leg height for an adult and anywhere on the kids!