Specialties of Models of the 6-dimensional Cube

We can have several procedures to construct 3-dimensional models of the more-dimensional cubes and 2-dimensional shadows of these, even on the classical field of Platonic and Archimedean solids. The polar zonohedron models of the more-dimensional cubes can be produced either as ray-groups based on symmetrical arranged starting edges or as sequences of bar-chains joining helices. The suitable combinations of the models can result in spatial tessellations. The shadows of the models and the sections of the mosaics allow unlimited possibilities to produce planar tessellations. The moved sectional planes result in series of tiling or grid-patterns transforming into each other. Working with these methods and in search for general algorithms, we may see, even from different approaches that the 6-dimensional cube’s models and their projections have more regular and more special features than those of other more-dimensional cubes and have several possibilities of application in different branches of art and design. We can find several procedures to construct 3-dimensional models (3-model) of the more-dimensional cubes (k-cubes) and 2-dimensional shadows of these. The next method of the modeling of k-cubes origins from a 3-dimensional reconstruction of the well known, regular octagon shaped shadow (Petrie polygon [12]) of the 4-cube [5]. Due to this result, the planar shadow of the 6-cube’s 3-model can be a regular dodecagon too. Figure 1 shows the reconstructed model (with and without faces) in top and elevation views.