Shapes of Constant Width
Use LEFT and RIGHT arrows to change the number of vertices and see various shapes of constant width that behave just as well as a circle would in this situation.
Wheels are circular because as you rotate them their width stays the same and so you have a smooth ride.
But a circle is not the only shape with that property. In fact, any shape with an odd number of vertices can have a constant width. Although they have corners and edges they make perfectly good wheels. See this video for example: https://youtu.be/270qEZKXAfQ?t=152
It's easy to make a shape of constant width with a compass. You put the point of the compass at one of the vertices and you round off the opposite face.