The quaternion group as a symmetry group

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Vi Hart and Henry Segerman: The quaternion group as a symmetry group. In: Bridges 2014. Pages 143–150



We briefly review the distinction between abstract groups and symmetry groups of objects, and discuss the question of which groups have appeared as the symmetry groups of physical objects. To our knowledge, the quaternion group (a beautiful group with eight elements) has not appeared in this fashion. We describe the quaternion group, both formally and intuitively, and give our strategy for representing the quaternion group as the symmetry group of a physical sculpture.

Extended Abstract


Used References

[1] John H. Conway, Heidi Burgiel, and Chaim Goodman-Strauss. The Symmetries of Things. A K Peters Ltd., 2008.

[2] John H. Conway and Derek A. Smith. On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. A K Peters Ltd., 2003.

[3] Gwen L. Fisher. The quaternions quilts. Focus: Newsletter of the MAA, 25(4):4, January 2005.

[4] Branko Gr ̈unbaum. What symmetry groups are present in the Alhambra? Notices of the AMS, 53(6):670– 673, 2006.

[5] Saul Schleimer and Henry Segerman. Sculptures in S3 . In Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture, pages 103–110, Phoenix, Arizona, 2012. Tessellations Publishing. Available online at


Full Text

intern file

Sonstige Links