Type: Article

Cubic tessellations of the didicosm

Hubard, Isabel; Mixer, Mark; Pellicer, Daniel; et al.;

Abstract:

Up to isomorphism, there is a unique fixed-point-free crystallographic group generated by two (2-fold) twists whose non-intersecting axes have perpendicular directions. Identifying points in E-3 which are in the same orbit under the action of this group yields the flat, closed 3-manifold known as the didicosm (also as the Hantzsche-Wendt manifold). When this group is realized as a group of symmetries of the standard cubical tessellation in E-3, the resulting quotient gives a cubical tessellation on the didicosm. This paper describes a complete classification of these cubical tessellations on the didicosm into ten classes, according to their automorphism groups.