This is a millinery hat block, the foundation for all hand made hats. After it is printed out, a velour hat body would be steamed and stretched over it, and left to dry. Once removed, it will keep the shape of the block. The mad hatter flare means that once the velour dried it would be impossible to remove the block without damaging the shape, so a 6-piece puzzle block allows the middle to be removed and the remaining pieces to collapse inward.