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Topology"],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study a remarkable simplicial complex <jats:italic>X<\/jats:italic> on countably many vertexes. <jats:italic>X<\/jats:italic> is <jats:italic>universal<\/jats:italic> in the sense that any countable simplicial complex is an induced subcomplex of <jats:italic>X<\/jats:italic>. Additionally, <jats:italic>X<\/jats:italic> is <jats:italic>homogeneous<\/jats:italic>, i.e. any two isomorphic finite induced subcomplexes are related by an automorphism of <jats:italic>X<\/jats:italic>. We prove that <jats:italic>X<\/jats:italic> is the unique simplicial complex which is both universal and homogeneous. The 1-skeleton of <jats:italic>X<\/jats:italic> is the well-known Rado graph. We show that a random simplicial complex on countably many vertexes is isomorphic to <jats:italic>X<\/jats:italic> with probability 1. We prove that the geometric realisation of <jats:italic>X<\/jats:italic> is homeomorphic to an infinite dimensional simplex. We observe several curious properties of <jats:italic>X<\/jats:italic>, for example we show that <jats:italic>X<\/jats:italic> is <jats:italic>robust<\/jats:italic>, i.e. removing any finite set of simplexes leaves a simplicial complex isomorphic to <jats:italic>X<\/jats:italic>. The robustness of <jats:italic>X<\/jats:italic> leads to the hope that suitable finite approximations of <jats:italic>X<\/jats:italic> can serve as models for very resilient networks in real life applications. In a forthcoming paper (Even-Zohar et al. Ample simplicial complexes, <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"http:\/\/arxiv.org\/abs\/2012.01483\">arXiv:2012.01483<\/jats:ext-link>, 2020) we study finite approximations to the Rado complex, they can potentially be useful in real life applications due to their structural stability.\n<\/jats:p>","DOI":"10.1007\/s41468-021-00069-z","type":"journal-article","created":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T05:03:15Z","timestamp":1620277395000},"page":"339-356","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Rado simplicial complex"],"prefix":"10.1007","volume":"5","author":[{"given":"Michael","family":"Farber","sequence":"first","affiliation":[]},{"given":"Lewis","family":"Mead","sequence":"additional","affiliation":[]},{"given":"Lewin","family":"Strauss","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,6]]},"reference":[{"key":"69_CR1","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/BF01594179","volume":"114","author":"W Ackermann","year":"1937","unstructured":"Ackermann, W.: Die Widerspruchsfreiheit der allgemeinen Mengenlehre. 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