PABICH Bronek

The family of uniform polyhedra

Few mathematicians in geometry deal with homogeneous polyhedra. Many of my friends, serious mathematicians find these polyhedrons difficult to create and do not see their use in other fields of knowledge. Hence, little interest in this issue.
However, these polyhedrons are so captivating and beautiful, they require so much hard thought on how to create cardboard models or 3D prints of them.
They were mostly created in the 20th century. They are somewhat analogous to what Archimedean polyhedra are to Platonic polyhedra, with the difference that we now allow faces to be non-convex polygons. There are 54 of them in total, but the last ones were discovered in the 1970s and are very complicated.
In my presentation, on the example of one of the uniform polyhedra, I will show the principle of their construction and I will show the ones whose models I made with my students.


3D printing as a teaching tool in mathematics teaching

Nowadays, many of us know what 3D printing, its design and other technical details are all about. However, it is worth considering how 3D printing can help teach geometry, especially spatial geometry, and even make it easier for students to discover algebraic patterns of abbreviated multiplication.
In my presentation, I will show numerous 3D models, the purpose of which is to better assimilate concepts such as the duality of polyhedrons, stellations, quick determination of the volume of selected solids, the search for geometric relationships between them and the development of students´ spatial imagination by preparing numerous puzzles and 3D puzzles.
All this happens with the participation of a computer that, by designing these numerous spatial structures, teaches the basic geometry of the compass and ruler, because these tools are used when designing these 3D creations in the GeoGebra and SketchUp software.