Trash Can Cover (AR Modeling Challenge)

[b]Students: [/b][br][br]How can we reconstruct the surface seen (in the screencast below) using only 2 surface equations? [br]Take these clues and see if you can reconstruct this surface in GeoGebra Augmented Reality! [br][br][b]Clues:[/b][br][br]This surface consists of 4 isosceles trapezoids. [br]The shorter base of each trapezoid is 6 units long. [br]The z-axis passes through the center of the square. [br]If all four planes were extended indefinitely, they would intersect at (0,0,5). [br]The projection of any slant edge onto the plane z = 0 lies along one of the lines [math]\left|y\right|=\left|x\right|[/math]. [br]The cross section of a [b][color=#1e84cc]blue plane[/color][/b] with any plane parallel to the plane y = 0 is a line that has [math]\left|\frac{\bigtriangleup z}{\bigtriangleup x}\right|=0.5[/math]. [br]The cross section of a [b][color=#ff00ff]pink plane[/color][/b] with any plane parallel to the plane x = 0 is a line that has [math]\left|\frac{\bigtriangleup z}{\bigtriangleup y}\right|=0.5[/math].

Information: Trash Can Cover (AR Modeling Challenge)