“di - knife” and the Process of Cutting of GRT(m.n) Bodies

Author: Ilia Tavkhelidze
Co-authors: Johan Gielis (Belgium)
Keywords: Generalized Rotated and Twisted bodies, di-knife
Annotation:

In this report, we consider GRT_m^n (Generalized Rotated and Twisted bodies which were analytically described in 2006 by Paolo Emilio Ricci and Ilia Tavkhelidze) and the cutting of these bodies using a “d_i-knife” (as defined by Johan Gielis and Ilia Tavkhelidze in 2018 with i = 1,2 ...,m, divisors of the number m). We will show how many independent objects appear after one complete cut with such knives along the basic line of the described bodies. The number of independent bodies depends on m and on its divisors, but never depends on the number of torsion n, unlike the case with GML_m^n – Generalized Mӧbius-Listing’s bodies.