{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:01Z","timestamp":1753893841890,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We construct a class of polycubes that tile the space by translation in a lattice-periodic way  and show that for this class the number of surrounding tiles cannot be bounded. The first  construction is based on polycubes with an $L$-shape but with many distinct tilings of the  space. Nevertheless, we are able to construct a class of more complicated polycubes such that  each polycube tiles the space in a unique way and such that the number of faces is $4k+8$ where  $2k+1$ is the volume of the polycube. This shows that the number of tiles that surround the  surface of a space-filler cannot be bounded.<\/jats:p>","DOI":"10.37236\/686","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:41:11Z","timestamp":1578714071000},"source":"Crossref","is-referenced-by-count":1,"title":["How many Faces can the Polycubes of Lattice Tilings by Translation of ${\\mathbb R}^3$ have?"],"prefix":"10.37236","volume":"18","author":[{"given":"I.","family":"Gambini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L.","family":"Vuillon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,10,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p199\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p199\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:01:05Z","timestamp":1579302065000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p199"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/686","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,10,10]]},"article-number":"P199"}}