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Platonic configurations of points and lines
Jurij Kovič, Aleksander Simonič, 2026, original scientific article

Abstract: We present some methods for constructing connected spatial geometric configurations (p_q, n_k) of points and lines, preserved by the same isometries of Euclidean space E³ as the predetermined Platonic solid. In this paper, we are mainly interested in configurations (n₃), (n₄), and (n₅), but also in unbalanced configurations (p₃, n₄), (p₃, n₅), and (p₄, n₅).
Keywords: configuration of points and lines, symmetry group, Platonic solid, centrally symmetric solid, projection from a point
Published in RUP: 22.12.2025; Views: 636; Downloads: 3
Full text (533,56 KB)

Splittable and unsplittable graphs and configurations
Nino Bašić, Jan Grošelj, Branko Grünbaum, Tomaž Pisanski, 2019, original scientific article

Abstract: We prove that there exist infinitely many splittable and also infinitely many unsplittable cyclic ▫$(n_3)$▫ configurations. We also present a complete study of trivalent cyclic Haar graphs on at most 60 vertices with respect to splittability. Finally, we show that all cyclic flag-transitive configurations with the exception of the Fano plane and the Möbius-Kantor configuration are splittable.
Keywords: configuration of points and lines, unsplittable configuration, unsplittable graph, independent set, Levi graph, Grünbaum graph, splitting type, cyclic Haar graph
Published in RUP: 03.01.2022; Views: 3065; Downloads: 31
Full text (355,79 KB)

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