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<p>The concept of an <i>n</i>-NTT (neighborly translational tessellation of the <i>n</i>-torus) is introduced as a tessellation where every pair of tiles are translates of each other, and share precisely one of their facets. An <i>n</i>-NTT with cubic tiles is studied for each <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10_2025_1162_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(n \in \mathbb {N}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </math></EquationSource> </InlineEquation>, and particular attention is given to a 4-NTT whose tiles are isometric 24-cells. We also use this concept to describe a tessellation of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10_2025_1162_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {E}^4\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">E</mi> </mrow> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation> with isometric tiles with fractal boundary, as well as a NTT of an infinite-dimensional space.</p>

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Neighborly translational tessellations of the n-torus

  • 期刊论文

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  • 发表日期：

    2025年5月20日

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  • Daniel Asimov,
  • Daniel Pellicer

摘要

The concept of an n-NTT (neighborly translational tessellation of the n-torus) is introduced as a tessellation where every pair of tiles are translates of each other, and share precisely one of their facets. An n-NTT with cubic tiles is studied for each \(n \in \mathbb {N}\) n ∈ N , and particular attention is given to a 4-NTT whose tiles are isometric 24-cells. We also use this concept to describe a tessellation of \(\mathbb {E}^4\) E 4 with isometric tiles with fractal boundary, as well as a NTT of an infinite-dimensional space.