30-Celled Collapsoid

Jean Pedersen discovered collapsoids while exploring a new way to make zonohedra (e.g. the rhombic dodecahedron and triacontahedron) out of pyramids. Her children played with an unfinished model of hers and discovered that it folds up. This 30-celled model has two variants that fold up in different ways.

Steps

1. Cut out 30 copies of the pattern piece from paper.
   
2. Score, fold and glue the pieces to form 30 baseless pyramids.
   
3. Tape the pyramids together by the open edges as shown.
   
4. Tape the edges using one of the two different options shown here. The top option allows the collapsoid to flatten from two poles to make a decagon (shown in the top inset of the photo above). The second option allows the collapsoid to "unroll" to make part of a decagon (bottom inset).
   

References

• (Pedersen, 1975)