3 papers
math.GT2020
Discrete geometry and topology of entanglement of straight lines in 3-space
Peter V Pikhitsa, Stanislaw Pikhitsa
We propose an unexpected twist to description of the geometry and topology of configurations of n straight lines considered as a whole 3D entity (because the lines are inseparably…
math.MG2017
Mutually touching infinite cylinders in the 3D world of lines
Peter V. Pikhitsa, Stanislaw Pikhitsa
Recently we gave arguments that only two unique topologically different configurations of 7 equal all mutually touching round cylinders (the configurations being mirror reflections…
math.MG2016
Symmetry, topology and the maximum number of mutually pairwise touching infinite cylinders: complete configuration classification
Peter V. Pikhitsa, Stanislaw Pikhitsa
We provide a complete classification of possible configurations of mutually pairwise touching infinite cylinders in Euclidian 3D space. It turns out that there is a maximum number…