The net of a cylinder is a rectangle for the curved side, with a circle touching it top and bottom. The rectangle is as wide as the base circumference, 2πr for radius r, and as tall as the cylinder itself. The cylinder here has radius 1 and height 2, so the side is a rectangle 2π wide and 2 tall.
Unlike a polyhedron, the curved side is not flat. It is cut into 48 thin strips, and neighbouring strips fold against each other a little at a time to roll into a tube. Each strip turns 360 degrees divided by 48, that is 7.5 degrees, so the seams disappear at a glance and the surface reads as a smooth curve.
The two circles lift through a right angle about the lines where they touch the top and bottom edges of the rectangle. The rolled side touches the tube along those lines, so lifting at a right angle points each circle exactly the way the top and bottom faces point, and their centres land on the axis of the tube. The display panel changes how fast it opens.