A new way of understanding the structure of proteins, polymers, minerals, and engineered materials has been discovered. The discovery, a new type of symmetry in the structure of materials, greatly expands the possibilities for discovering or designing materials with desired properties. The research is expected to have broad relevance in many development efforts involving physical, chemical, biological, or engineering disciplines, including the search for advanced ferroelectric ferromagnet materials for next-generation ultrasound devices and computers.