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

Katja Berčič; Gabe Cunningham; Andrés David Santamaría-Galvis; Janoš Vidali

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

Combinatorics 2026-06-26 v1

Authors: Katja Berčič , Gabe Cunningham , Andrés David Santamaría-Galvis , Janoš Vidali

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.

Cite

@article{arxiv.2606.27987,
  title  = {Maniplexes as a Foundation for Cross-Linked Databases of Symmetric Objects},
  author = {Katja Berčič and Gabe Cunningham and Andrés David Santamaría-Galvis and Janoš Vidali},
  journal= {arXiv preprint arXiv:2606.27987},
  year   = {2026}
}

Comments

Submitted (pre-peer-review) version. Accepted at CICM 2026; the Version of Record will appear in Springer LNAI. We'll add the DOI once the proceedings are published