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Step 1: Materials/Techniques
You can use either EVA Y-20 foam (ethylene vinyl acetate) or XLPE (Cross-linked polyethylene foam). Both are similar to yoga mat material, suitable for use with hot glue or contact cement, come in a big range of thicknesses for stiffness, and after sealing can be painted if needed. For the strongest permanent bond always use contact cement. Follow the instructions and allow it to dry to a dull finish for ~15 minutes to get maximum grab.
You can cut the foam rubber one of three ways depending on the type of cut:
Scissors: Better on thick material but may leave a rough serrated edge.
Long box cutter: gives a clean edge.
Hot knife: Works well on thin material with very tight contours.
I've price shopped the entire internet. Cheapest foam: http://www.thefoamfactory.com/closedcellfoam/cross-linked-polyethylene-foam.html. My local fabric store, Joann's Fabrics, always has a weekly 50% off coupon that cuts cost on the fur which is $20/yrd.
Step 2: Foam Substructure
You can see the standard sheet width is the middle portion and that an extra portion had to be added to hit the 7 foot width. The foam was cut with a fresh very sharp razor blade. In general I recommend buying a pack of 50 blades so you don't tear and pull at the rubber with a dull edge.
Contact cement was spread around the rim of each side except for the lower central bottom since that is where you'll get in the costume. The contact cement is allowed to dry at least 15 minutes and then the surfaces are pressed together with firm pressure for several seconds. I then created foam tubing from foam pipe insulation to add to the 3D shape of the costume. It was then glued into place.
Step 3: Upholstery
Step 4: How to Wear It?
Slits were cut in the area where nostrils would be found and a flap of fabric was added to hide the cutout. That way you can hide the arms to give a clean mustache profile or put them out for a cartoon character feel.
An eye hole was cut and black mesh was added to the back.
Step 5: Finishing Details
If you have any questions on how to build your own costume, feel free to ask in the comments and I'll do my best to help.