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<p>In this paper, we study simple face-based indices for both two-dimensional tilings and a real three-dimensional material. First, we derive the face index and the face neighbourhood index for finite patches of the octagon–square tiling and compare how these indices change with the size and shape of the patch. Next, we extend the idea of the face index to titania (TiO<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_2\)</EquationSource> </InlineEquation>) by viewing its crystal structure as a network of polyhedral units and computing the corresponding face contributions. These results show that face-based indices can capture useful structural information in both ideal planar lattices and realistic inorganic frameworks.</p>

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Computation of face indices for octagon tilings and titania nanostructures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月28日

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  • Raghav Verma,
  • Vijay Kumar Bhat

摘要

In this paper, we study simple face-based indices for both two-dimensional tilings and a real three-dimensional material. First, we derive the face index and the face neighbourhood index for finite patches of the octagon–square tiling and compare how these indices change with the size and shape of the patch. Next, we extend the idea of the face index to titania (TiO \(_2\) ) by viewing its crystal structure as a network of polyhedral units and computing the corresponding face contributions. These results show that face-based indices can capture useful structural information in both ideal planar lattices and realistic inorganic frameworks.