How do I build a universal reflector? I would like to make one for a
school physics project.I want to make it out of three identical square
plan mirrors that will glued together to form three adjacent sides of
a cube meeting at a corner, with the mirrored sides all facing towards
each other. A simple illustration would help.

Good luck on your project.

Corner reflector
http://www.exploratorium.edu/snacks/corner_reflector.html

Light/corner reflectors
http://muller.lbl.gov/teaching/Physics10/chapters/11-Light.html

MIRRORS AND ETALONS
http://cord.org/cm/leot/course06_mod05/mod06_05.htm

Virtual images formed by intersecting plane mirrors 
http://learning.physics.iastate.edu/DemoRoom/Light/Light-2.htm

Mirrors - Large Corner Cube Reflector 
http://www.physics.uiowa.edu/~dstille/optics/6A10.31.htm

Highly Stable Lateral-Transfer Retroreflectors
http://www.nasatech.com/Briefs/Mar99/GSC14056.html

The SLAC Design and Manufacturing Process of Sphere-Mounted Reflectors
http://www.slac.stanford.edu/grp/met/TOC_S/Papers/BFuss97a.pdf

Measuring the Moon's Distance
http://sunearth.gsfc.nasa.gov/eclipse/SEhelp/ApolloLaser.html

Satellite Laser Ranging (SLR)
http://rst.gsfc.nasa.gov/Intro/Part2_1c.html

Project Starshine
http://www.azinet.com/starshine/

Hollow Retroreflectors
http://www.edmundoptics.com/IOD/DisplayProduct.cfm?productid=1943

Wow! Thanks for that ulu-ga!

You might want to protect the mirrors by putting them in the corner of
a wooden or cardboard box.  Plastic mirrors were recommended by one of
the web pages.  If you do use glass, you might want to tape all the
exposed edges to reduce the risk of cuts.

If you don't use a separate base, putting both of the vertical mirrors
on top of the horizontal mirror would give it more support.

Front (or first) surface mirrors are best but are probably harder (and
more expensive) to get.  The reflective material is not behind the
distorting glass or plastic.  Because the reflective surface is
exposed, it is more likely to get damaged.

Some of the references listed can be quite technical.  Don't get
overwhelmed from the details.

If you use a laser pointer, be extra careful with the reflections.

Terrestrial Surveying Application (not all of them are on the moon)
http://www.leica-geosystems.com/ims/product/tps5000_reflectors.htm

Again, good luck with your project and have fun!

If you've got a ZIP disk, it should have a small array of corner cubes
on it.  I can't remember if it's the 100 MB, 250 MB, or both.  It
might be just the thing if you're using a laser pointer.