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Although neither of the two yields observable-based contextual configurations of their own,  <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>c<\/mml:mi><mml:mi>l<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>s<\/mml:mi><mml:mi>s<\/mml:mi><mml:mi>i<\/mml:mi><mml:mi>c<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>l<\/mml:mi><mml:mi>l<\/mml:mi><mml:mi>y<\/mml:mi><\/mml:math>-embedded copies are found to fully encode contextuality properties of the most prominent three-qubit contextual configurations in the following sense: for each set of unsatisfiable contexts of such a contextual configuration there exists some classically-embedded hexagon sharing with the configuration exactly this set of contexts and nothing else. We demonstrate this fascinating property first on the configuration comprising all 315 contexts of the space and then on doilies, both types of quadrics as well as on complements of skew-embedded hexagons. In connection with the last-mentioned case and elliptic quadrics we also conducted some experimental tests on a Noisy Intermediate Scale Quantum (NISQ) computer to substantiate our theoretical findings.<\/jats:p>","DOI":"10.22331\/q-2025-01-20-1601","type":"journal-article","created":{"date-parts":[[2025,1,20]],"date-time":"2025-01-20T15:07:21Z","timestamp":1737385641000},"page":"1601","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Hexagons govern three-qubit contextuality"],"prefix":"10.22331","volume":"9","author":[{"given":"Metod","family":"Saniga","sequence":"first","affiliation":[{"name":"Astronomical Institute of the Slovak Academy of Sciences, SK-05960 Tatransk\u00e1 Lomnica, Slovakia"}]},{"given":"Fr\u00e9d\u00e9ric","family":"Holweck","sequence":"additional","affiliation":[{"name":"Laboratoire Interdisciplinaire Carnot de Bourgogne, ICB\/UTBM, UMR 6303, CNRS, Universit\u00e9 de Technologie de Belfort-Montb\u00e9liard, F-90010 Belfort Cedex, France"},{"name":"Department of Mathematics and Statistics, Auburn University, Auburn, AL, USA"}]},{"given":"Colm","family":"Kelleher","sequence":"additional","affiliation":[{"name":"Laboratoire Interdisciplinaire Carnot de Bourgogne, ICB\/UTBM, UMR 6303, CNRS, Universit\u00e9 de Technologie de Belfort-Montb\u00e9liard, F-90010 Belfort Cedex, France"}]},{"given":"Axel","family":"Muller","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Marie et Louis Pasteur, CNRS, Institut FEMTO-ST, F-25000 Besan\u00e7on, France"}]},{"given":"Alain","family":"Giorgetti","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Marie et Louis Pasteur, CNRS, Institut FEMTO-ST, F-25000 Besan\u00e7on, France"}]},{"given":"Henri de","family":"Boutray","sequence":"additional","affiliation":[{"name":"ColibriTD, F-75013 Paris, France"}]}],"member":"9598","published-online":{"date-parts":[[2025,1,20]]},"reference":[{"key":"0","unstructured":"IBM Quantum Experience. https:\/\/quantum-computing.ibm.com\/."},{"key":"1","doi-asserted-by":"publisher","unstructured":"D. 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