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Vol. 31 No. 1 (2026)

Regular Articles

Exploring the configurations $(12_4, 16_3)$ of Václav Metelka in a cubic structure

https://doi.org/10.64785/mc.31.1.2

Published 2025-11-05

  • Vladimir Volenec
    • ,
  • Ružica Kolar-Šuper

Vladimir Volenec
Department of Mathematics, Faculty of Science and Mathematics, Zagreb

Ružica Kolar-Šuper
Faculty of Education, Department of Natural Sciences, University of Osijek

Abstract

In this paper, we investigate four configurations $(12_4, 16_3)$ in cubic structures, introduced by Václav Metelka, and discover new unexpected extra collinearities in two Metelka's configurations that arise from our realizations in cubic structures. Next, we establish the existence of various geometric concepts in three Metelka's configuration including tangential points, inflection points, sextactic points, and quadrilaterals, and find and study significant relationships among these geometric concepts. Finally, we demonstrate that the fourth Metelka's configuration cannot be embedded into any cubic structure.

Keywords

configuration $(12_4, 16_3)$, cubic structure, tangential of a point, inflection point

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Author Biography

Ružica Kolar-Šuper

Ružica Kolar-Šuper is a Full Professor in the Department of Natural Sciences, Sub-Department of Mathematics at Faculty of Education, University of Osijek. Her research focuses on geometry and non-associative algebraic structures.