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On the contrary, we show that for every polygonal norm (that is, the unit ball is a polygon) in the plane, there exists an infinite <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathcal {M}\\subset \\mathbb {R}^2$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>M<\/mml:mi>\n                    <mml:mo>\u2282<\/mml:mo>\n                    <mml:msup>\n                      <mml:mrow>\n                        <mml:mi>R<\/mml:mi>\n                      <\/mml:mrow>\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:msup>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> such that for every two-colouring of the plane there exists a monochromatic isometric copy of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathcal {M}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>M<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s00454-024-00702-5","type":"journal-article","created":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T13:53:13Z","timestamp":1731419593000},"page":"569-583","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Monochromatic Infinite Sets in Minkowski Planes"],"prefix":"10.1007","volume":"74","author":[{"given":"N\u00f3ra","family":"Frankl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-2367-6314","authenticated-orcid":false,"given":"Panna","family":"Geh\u00e9r","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arsenii","family":"Sagdeev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00e9za","family":"T\u00f3th","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,11,12]]},"reference":[{"issue":"3","key":"702_CR1","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/BF00181411","volume":"37","author":"KB Chilakamarri","year":"1991","unstructured":"Chilakamarri, K.B.: Unit-distance graphs in Minkowski metric spaces. 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