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arXiv · 2606.27987

Maniplexes as a Foundation for Cross-Linked Databases of Symmetric Objects

Katja Berčič·Gabe Cunningham·Andrés David Santamaría-Galvis·Janoš Vidali
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Abstract

Graphs, maps on surfaces, and abstract polytopes are related combinatorial structures that tend to be studied by different communities using their own tools and databases. Maniplexes provide a unifying framework that captures all of them. A single database built around maniplexes would help researchers recognize shared structures and translate results across fields. Here we present a compact, interoperable format for storing maniplexes as edge-labeled graphs, designed with such a database in mind. As a first step, we connect two existing datasets of regular 4-maniplexes to the House of Graphs and to Poto\v{c}nik's tetravalent graph censuses, using canonical forms of their flag graphs, 1-skeleton graphs, and 1-coskeleton graphs.

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Katja Berčič, Gabe Cunningham, Andrés David Santamaría-Galvis, Janoš Vidali. 2026-06-26. Maniplexes as a Foundation for Cross-Linked Databases of Symmetric Objects. https://arxiv.org/abs/2606.27987

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