An interview with Krisztina Regős, graduate student of the Faculty of Architecture of BME and her supervisor, Gábor Domokos has recently been published at forbes.hu.
The conversation reveals how Gömböc inspires young researchers, specifically how this discovery influenced Krisztina’s further research.
A two-vertex theorem for normal tilings
Gábor Domokos, Ákos G. Horváth, Krisztina Regős
Abstract: We regard a smooth, 𝑑=2-dimensional manifold ℳ and its normal tiling M, the cells of which may have non-smooth or smooth vertices (at the latter, two edges meet at 180 degrees.) We denote the average number (per cell) of non-smooth vertices by 𝑣¯⋆ and we prove that if M is periodic then 𝑣¯⋆≥2. We show the same result for the monohedral case by an entirely different argument. Our theory also makes a closely related prediction for non-periodic tilings. In 3 dimensions we show a monohedral construction with 𝑣¯⋆=0.