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It is called\n                    <jats:italic>n<\/jats:italic>\n                    -gc-self-affine if the dissection is obtained by successive glass-cuts, which are cuts along segments splitting one disc into two. For every\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$n \\ge 2$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\u2265<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , we characterize all\n                    <jats:italic>n<\/jats:italic>\n                    -gc-self-affine discs. All such discs turn out to be either triangles or convex quadrangles. All triangles and trapezoids are\n                    <jats:italic>n<\/jats:italic>\n                    -gc-self-affine for every\n                    <jats:italic>n<\/jats:italic>\n                    . Non-trapezoidal quadrangles are not\n                    <jats:italic>n<\/jats:italic>\n                    -gc-self-affine for even\n                    <jats:italic>n<\/jats:italic>\n                    . They are\n                    <jats:italic>n<\/jats:italic>\n                    -gc-self-affine for every odd\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$n \\ge 7$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\u2265<\/mml:mo>\n                            <mml:mn>7<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , and they are\n                    <jats:italic>n<\/jats:italic>\n                    -gc-self-affine for\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$n=5$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>5<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    if they aren\u2019t affine kites. Only four one-parameter families of quadrangles turn out to be 3-gc-self-affine. In addition, we show that every convex quadrangle is\n                    <jats:italic>n<\/jats:italic>\n                    -self-affine for all\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$n \\ge 5.$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\u2265<\/mml:mo>\n                            <mml:mn>5<\/mml:mn>\n                            <mml:mo>.<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                  <\/jats:p>","DOI":"10.1007\/s00454-025-00777-8","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T15:49:43Z","timestamp":1760543383000},"page":"466-490","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Self-Affinity of Discs Under Glass-Cut Dissections"],"prefix":"10.1007","volume":"76","author":[{"given":"Christian","family":"Richter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,10,15]]},"reference":[{"key":"777_CR1","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/BF02568049","volume":"22","author":"B Bernheim","year":"1949","unstructured":"Bernheim, B., Motzkin, T.: A criterion for divisibility of $$n$$-gons into $$k$$-gons. 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