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Using a construction method where all nodes are placed in a single one-dimensional space and the connections lie in coordinate planes, we show that it is possible to robustly realize these networks in R6 for any number of nodes n using a polynomial vector field. This bound on the space dimension (while the number of nodes in the network goes to \u221e) is a novel phenomenon and a step toward more efficient realization methods for given connection structures in terms of the required number of space dimensions. We briefly discuss some stability properties of the generated heteroclinic objects.<\/jats:p>","DOI":"10.1063\/5.0156192","type":"journal-article","created":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T06:15:22Z","timestamp":1693376122000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Arbitrarily large heteroclinic networks in fixed low-dimensional state space"],"prefix":"10.1063","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9029-6893","authenticated-orcid":false,"given":"Sofia B. S. 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