UPDATE: added a Dual extrusion version - prints the same without support and looks even better!
This is my design for the 2014 Thingiverse Make-A-Thon and it won me first place! It prints with no supports within a 50mm^3 space. Once assembled, you simply rotate the nautilus shell to the desired angle and set your phone in, resting its back on the shell, keeping captive with the lip at the front.
Prints great at .2mm layer heigh, standard speeds and feeds. This was printed on 5th gen makerbot machines in PLA, and worked well at layer heights of .3mm as well.
Once printed, remove the two retaining pins from the bottom of the base. They should come out with little effort, but this may be adjusted in the future. Take the Nautilus shell, and place it horizontally in the base. Insert the pins carefully on either side of the indented surfaces in the center of the shell piece. they only go in one way, and should friction fit. the pins are in place when the tabs on the end of the pins fall into the cutouts on the rear of the base. Finally, crack loose the front 'jaw' on the print to allow your phone to have a nice rest on the beach.
make one and post it back here!