I printed the "2001_TMA-1_base+Support" in ABS @ 235 degrees C, which resulted in minor warping of the base despite my use of a heated bed @ 110C. After the supports were removed, the model was cleaned up a little (not enough, really) and painted with acrylics.
To use: run your phone's charging cable through the hole in the base, then insert the phone, preferably during a major planetary alignment.
I used Netfabb to remove the glass from the astronaut's helmet in order to better show the face, then I used the program's Z cut function to reduce the height of the base. Other issues with the mesh were fixed in 3D Builder, then supports were added with Meshmixer.
Optional: Print "helmet_window.stl" in T-Glase or transparent PLA and glue in place.