Portraits of Groups in Three Dimensions

Jay Zimmerman and Kevin Zimmerman
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 413–414 Short Papers


This paper looks at the sculptures that result from representing a group G of order 8 as a group of three dimensional transformations. The action is realized as a quotient of a full quadrilateral group and so all cells have four edges. We use tetrahedra to represent the regions and each cell is adjacent to four others. The model of this 3-manifold in space must have a boundary. These sculptures are dynamic in the sense that each cell on this boundary may be moved to another part of the boundary to give a different sculpture.