Can you author 2 surface equations (with possible domain restrictions) to reconstruct this 2-faced virtual ice cream cone within GeoGebra Augmented Reality? [br][br][b]Clues:[br][br][/b]1) The blue surface is a hemisphere with radius = 3. [br][br]2) The top point of the hemisphere is (0, 0, 5).[br][br]3) The apex of the cone is at (0,0,5).[br][br]4) The projection of all 4 eyes onto the plane z = 0 are circles with centers [math]\left(\pm0.8,\pm1.5\right)[/math] and [math]r=\frac{\sqrt{10}}{10}[/math]. [br][br]5) The projection of the one mouth boundary onto the plane z = 0 has equation [math]y=0.09x^2-2.8[/math]. [br][br]6) The projection of the other mouth boundary onto the plane z = 0 has equation [math]y=-0.09x^2+2.8[/math]. [br][br][b]For additional challenges, see the text below this screencast. [/b]

1) Reconstruct this same surface, yet reflect it about the plane z = 0. [br] I.E: "Flip it upside down"! [br][br]2) Reconstruct this same surface, yet put 2 additional mouths on here that are the mouths seen here, yet [br] rotated [math]90^\circ[/math] about (0,0,0).