This is a challenging construction, but the results are worth the work!
Step 1: Fold the paper in half to create a "mountain fold" as shown below.
Step 2: Fold the paper in half again, to create four congruent squares.
Step 3: Fold one corner in so that its point lines up with the center of
the sheet of paper.
Step 4: Fold the opposite corner in the same way to create the shape
shown below.
Step 5: Fold the right edge up toward the center diagonal to create
the shape shown below.
Step 6: Fold the left edge toward the center diagonal in the same way
as shown below.
Step 7: Open the last two folds to see the shape shown below. Notice
the two parallel diagonal lines that have been formed.
Step 8a: Close the two side pieces to get back to this shape. The next
fold will create a crease that creates a line through the two points indicated
by the fingers in the photo.
Step 8b: Notice the fold, now in place.
Step 8c: Now fold that piece back, behind the shape as shown below.
Step 9: Repeat on the opposite corner to create the shape shown below.
Step 10: Fold the two "tags" (top right and lower left) into the shape.
Step 11: Open to see a rectangular shape as shown below.
Step 12a: The next fold will create a valley fold that runs through the
two points indicated by the fingers in the photo.
Step 12b: Notice the fold below, now in place. This is the finished unit!
Step 13: Now make 29 more units identical to the one shown above!
To construct the Great Stellated Dodecahedron:
The steps below are shown in three colors to make it easier to see
and understand the steps involved.
Step 1: Line two pieces up as shown below to be sure they are congruent.
Step 2a: Place the second piece, shown in blue, so that its first fold
lines up with the second fold of the original piece, shown in yellow.
Step 2b: Below is the top view of what is done in step 2a.
Step 3: The third piece will tuck into the second. Below the third
piece is shown in green, the second piece is shown in blue.
Step 4a: Now the first piece, shown in yellow, wraps around to tuck
into the third piece, shown in green.
Step 4b: See one completed pyramid below, which includes that
yellow tab tucked into the green piece from above. This will create
a pyramid that has a triangular base. You will also notice a "tail"
sticking out off of each side of the base.
Step 5: Now add on more pyramids to each of the "tails" using the
same process used to make the original pyramid. You will find that
five pyramids connect to make a star shape. This pattern will continue
all the way around the shape as it takes form!
Finished Super Stellated Dodecahedron