This is an easy octohedron that I found when looking around for a modular version. Sam Ciulla, the creator, uses only one paper as well as following the same concepts as the familiar water bomb. This provides a great introduction to preparation folding for beginners. I hope you enjoy the Instructable and be sure to leave a comment with any questions and/or improvements!
Step 1: Materials
What you need:
Step 2: Preliminary Folds Part One
Lay your sheet colored side up on work space. Fold in half, top down as shown. Now bring the top layer upwards to the center fold, Crease well and repeat on the other side to complete bookfold. Unfold completely, turn 90 degrees, and repeat. Your crease pattern should resemble the picture.
Step 3: Preliminary Folds Part Two
Turn paper 45 degrees to resemble a diamond. bring the top corner to the bottom to fold in half. Repeat vertically. Creases will look like picture above. Now comes the tedious part- fold every diagonal as shown in the above picture. I apologize for grease stains, little sis wanted to help ;-)
Step 4: Beginning Construction
Fold corners inward on the outermost diagonal, white side up. Bring sides inward to create a water bomb base as shown.
Step 5: Construction Continued
Fold the top layer over to center of diagonals as shown, then bring thick flap back. Crease well and repeat on all other flaps as shown.
Step 6: Final Step
Fold bottom corners over flaps as shown, then tuck into flap. Repeat on all sides.
Blow carefully into bottom hole in order to inflate the model.
Press all edges inward as shown. This can be hard to see but look at the model and it is easy to tell where to press the model in.
Step 7: All Done!!
Provided you have pushed all edges inward, the ball will form a stellated octohedron. This is a great model to show off as it seems impossible to have made it with just one sheet.