Menger Sponge Solution
How It Works
The first step is to put together the 20 individual cubes. This is done based on the instructions listed in the page and the video. The labels for each card go on the inside of the cube, and the directions are relative to you if you hold a cube up in front of you. That is, the side closest to you is "F", the side farthest from you is "Back", the side on the left of you is "L", and the side on your right is "R".
Once the cubes have been correctly built, teams need to assemble the 20 cubes into a Menger sponge as shown on the bottom right of the instruction page. There are three types of things that you might see on the surface of a cube - a card back, a black-bordered normal card face (every black-bordered card that a single team has will be identical, though that card is different across teams), or a white-bordered land face (Plains, Island, Swamp, Mountain, or Forest). They should quickly realize that the white-bordered lands are the join points. Putting cubes together by matching lands together, there is only a single way to build the Menger Sponge such that lands match at all points where cubes touch each other.
Once this has been done correctly, the card backs along each of the four sides spell a letter (the top and bottom have all card fronts and are not involved in the solution). Reading clockwise around the sides will yield the answer - COIL.
Solution
COIL