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Journal articles on the topic 'Spherical tilings'

Author: Grafiati

Published: 7 September 2021

Last updated: 29 July 2025

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1

AVELINO, CATARINA P., and ALTINO F. SANTOS. "DEFORMATION OF F-TILINGSVERSUSDEFORMATION OF ISOMETRIC FOLDINGS." International Journal of Mathematics 23, no. 09 (2012): 1250092. http://dx.doi.org/10.1142/s0129167x12500929.

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We present some relations between deformation of spherical isometric foldings and deformation of spherical f-tilings. The natural way to deform f-tilings is based on the Hausdorff metric on compact sets. It is conjectured that any f-tiling is (continuously) deformable in the standard f-tiling τs= {(x, y, z) ∈ S2: z = 0} and it is shown that the deformation of f-tilings does not induce a continuous deformation on its associated isometric foldings.

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2

Escudero, Juan Garcia. "Deltoid Tangents with Evenly Distributed Orientations and Random Tilings." Journal of Geometry and Symmetry in Physics 65 (March 30, 2023): 1–39. http://dx.doi.org/10.7546/jgsp-65-2023-1-39.

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We study the construction of substitution tilings of the plane based on certain simplicial configurations of tangents of the deltoid with evenly distributed orientations. The random tiling ensembles are obtained as a result of tile rearrangements in the substitution rules associated to edge flips. Special types of random tilings for Euclidean, spherical and hyperbolic three-manifolds are also considered.

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3

Max, Nelson. "Constructing and Visualizing Uniform Tilings." Computers 12, no. 10 (2023): 208. http://dx.doi.org/10.3390/computers12100208.

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This paper describes a system which takes user input of a pattern of regular polygons around one vertex and attempts to construct a uniform tiling with the same pattern at every vertex by adding one polygon at a time. The system constructs spherical, planar, or hyperbolic tilings when the sum of the interior angles of the user-specified regular polygons is respectively less than, equal to, or greater than 360∘. Other works have catalogued uniform tilings in tables and/or illustrations. In contrast, this system was developed as an interactive educational tool for people to learn about symmetry

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4

Escudero, Juan García. "Random tilings of spherical 3-manifolds." Journal of Geometry and Physics 58, no. 11 (2008): 1451–64. http://dx.doi.org/10.1016/j.geomphys.2008.05.015.

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5

Ribeiro, PatrÃcia, A. M. d. Azevedo Breda, and Robert Dawson. "Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 3 (2016): 5992–6014. http://dx.doi.org/10.24297/jam.v12i3.484.

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The study of spherical dihedral f-tilings when the prototiles are twononcongruent isosceles triangles was started in two previous papers. Here,we complete the classication, characterizing the f-tilings that satisfy theremaining case of adjacency. As it will be shown, this class is composed bytwo three-parameter families denoted by An;m; and Bn;m; and a relatedfour-parameter family denoted by Bp;q;pâ€²;qâ€², where p > pâ€² 0; qâ€²> q 0;two isolated tilings denoted by P and Q; and six distinct discrete familiesdenoted by J k;Lk; Mk;Nk(k 3); and Fk;Kk with k 4.

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6

Panina, G. Yu. "Pointed spherical tilings and hyperbolic virtual polytopes." Journal of Mathematical Sciences 175, no. 5 (2011): 591–99. http://dx.doi.org/10.1007/s10958-011-0374-y.

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7

Altino F. Santos. "A New Metric on Spherical f-Tilings." American Mathematical Monthly 122, no. 4 (2015): 354. http://dx.doi.org/10.4169/amer.math.monthly.122.04.354.

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8

d’Azevedo Breda, A. M., Patrícia S. Ribeiro, and Altino F. Santos. "A class of spherical dihedral f-tilings." European Journal of Combinatorics 30, no. 1 (2009): 119–32. http://dx.doi.org/10.1016/j.ejc.2008.02.010.

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9

Konevtsova, O. V., V. L. Lorman, and S. B. Rochal. "Structures of spherical viral capsids as quasicrystalline tilings." Physics of the Solid State 57, no. 4 (2015): 810–14. http://dx.doi.org/10.1134/s1063783415040125.

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10

Castle, Toen, Myfanwy E. Evans, Stephen T. Hyde, Stuart Ramsden, and Vanessa Robins. "Trading spaces: building three-dimensional nets from two-dimensional tilings." Interface Focus 2, no. 5 (2012): 555–66. http://dx.doi.org/10.1098/rsfs.2011.0115.

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We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic ( S 2 ), Euclidean ( E 2 ) and hyperbolic ( H 2 ) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab in

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11

Akama, Yohji, and Nico Van Cleemput. "Spherical tilings by congruent quadrangles: Forbidden cases and substructures." Ars Mathematica Contemporanea 8, no. 2 (2015): 297–318. http://dx.doi.org/10.26493/1855-3974.581.a6a.

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12

Sakano, Yudai, and Yohji Akama. "Anisohedral spherical triangles and classification of spherical tilings by congruent kites, darts and rhombi." Hiroshima Mathematical Journal 45, no. 3 (2015): 309–39. http://dx.doi.org/10.32917/hmj/1448323768.

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13

d'Azevedo Breda, Ana M., and José Dos Santos Dos Santos. "A new class of monohedral pentagonal spherical tilings with GeoGebra." Portugaliae Mathematica 74, no. 3 (2018): 257–66. http://dx.doi.org/10.4171/pm/2006.

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14

Avelino, Catarina P., and Altino F. Santos. "Spherical f-tilings by scalene triangles and isosceles trapezoids, II." Acta Mathematica Sinica, English Series 28, no. 5 (2011): 1013–32. http://dx.doi.org/10.1007/s10114-011-9511-2.

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15

Avelino, Catarina P., and Altino F. Santos. "Spherical f-tilings by scalene triangles and isosceles trapezoids, I." European Journal of Combinatorics 30, no. 5 (2009): 1221–44. http://dx.doi.org/10.1016/j.ejc.2008.12.021.

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16

Avelino, Catarina P., and Altino F. Santos. "Spherical f-Tilings by (Equilateral and Isosceles) Triangles and Isosceles Trapezoids." Annals of Combinatorics 15, no. 4 (2011): 565–96. http://dx.doi.org/10.1007/s00026-011-0110-9.

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17

d’Azevedo Breda, A. M., and Patrícia S. Ribeiro. "Deformation of a Class of Dihedral Spherical $$f\hbox {-}$$ f - Tilings." Bulletin of the Malaysian Mathematical Sciences Society 40, no. 1 (2016): 473–86. http://dx.doi.org/10.1007/s40840-016-0324-4.

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18

Breda, Ana, Robert Dawson, and Patrícia Ribeiro. "Spherical f-tilings by two noncongruent classes of isosceles triangles-II." Acta Mathematica Sinica, English Series 30, no. 8 (2014): 1435–64. http://dx.doi.org/10.1007/s10114-014-3302-5.

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19

CHEN, NING, and NANNAN LUO. "CONSTRUCTION OF SPHERICAL PATTERNS FROM PLANAR DYNAMIC SYSTEMS." Fractals 21, no. 01 (2013): 1350005. http://dx.doi.org/10.1142/s0218348x13500059.

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We investigated the generation of spherical continuous-tilings of the chaotic attractors or the filled-in Julia sets from the plane mappings. We build three plane mappings, which can be used to construct the continuous patterns on the surfaces of the hexahedron and the unit sphere. We discuss the coordinate transformation for a spatial point between the different coordinate systems and further discuss how to project a spherical point onto a surface of the inscribed hexahedron. We present a method of constructing a spherical pattern with the pattern of a square on the inscribed hexahedron from

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20

Akama, Yohji. "Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (I) -- a special tiling by congruent concave quadrangles." Hiroshima Mathematical Journal 43, no. 3 (2013): 285–304. http://dx.doi.org/10.32917/hmj/1389102577.

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21

Avelino, Catarina P., and Altino F. Santos. "Right Triangular Spherical Dihedral f–Tilings with Two Pairs of Congruent Sides." Applied Mathematics & Information Sciences 7, no. 3 (2013): 889–907. http://dx.doi.org/10.12785/amis/070307.

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22

Akama, Yohji. "Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (II)—the isohedral case." Hiroshima Mathematical Journal 49, no. 1 (2019): 1–34. http://dx.doi.org/10.32917/hmj/1554516036.

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23

Karner, Carina, Felix Müller, and Emanuela Bianchi. "A Matter of Size and Placement: Varying the Patch Size of Anisotropic Patchy Colloids." International Journal of Molecular Sciences 21, no. 22 (2020): 8621. http://dx.doi.org/10.3390/ijms21228621.

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Non-spherical colloids provided with well-defined bonding sites—often referred to as patches—are increasingly attracting the attention of materials scientists due to their ability to spontaneously assemble into tunable surface structures. The emergence of two-dimensional patterns with well-defined architectures is often controlled by the properties of the self-assembling building blocks, which can be either colloidal particles at the nano- and micro-scale or even molecules and macromolecules. In particular, the interplay between the particle shape and the patch topology gives rise to a plethor

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24

Breda, Ana, and José Dos Santos. "Spherical Tiling with GeoGebra." Resonance 24, no. 8 (2019): 861–73. http://dx.doi.org/10.1007/s12045-019-0849-6.

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25

Avelino, Catarina P., and Altino F. Santos. "Right triangular spherical dihedral f-tilings: the $${\left(\frac{\pi}{2},\frac{\pi}{3},\frac{\pi}{5}\right)}$$ , $${\left(\frac{\pi}{2},\frac{2\pi}{5},\frac{\pi}{5}\right)}$$ family." Journal of Geometry 102, no. 1-2 (2011): 1–17. http://dx.doi.org/10.1007/s00022-011-0101-3.

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26

Gao, Honghao, Nan Shi, and Min Yan. "Spherical tiling by 12 congruent pentagons." Journal of Combinatorial Theory, Series A 120, no. 4 (2013): 744–76. http://dx.doi.org/10.1016/j.jcta.2012.12.006.

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27

Bizzarri, Michal, Miroslav Lávička, Jan Vršek, Michael Bartoň, and Jiří Kosinka. "On tiling spherical triangles into quadratic subpatches." Computer Aided Geometric Design 111 (June 2024): 102344. http://dx.doi.org/10.1016/j.cagd.2024.102344.

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28

Efremov, A., T. Vereschagina, Nina Kadykova, and Vyacheslav Rustamyan. "Spatial Geometric Cells — Quasipolyhedra." Geometry & Graphics 9, no. 3 (2021): 30–38. http://dx.doi.org/10.12737/2308-4898-2021-9-3-30-38.

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Tiling of three-dimensional space is a very interesting and not yet fully explored type of tiling. Tiling by convex polyhedra has been partially investigated, for example, works [1, 15, 20] are devoted to tiling by various tetrahedra, once tiling realized by Platonic, Archimedean and Catalan bodies. The use of tiling begins from ancient times, on the plane with the creation of parquet floors and ornaments, in space - with the construction of houses, but even now new and new areas of applications of tiling are opening up, for example, a recent cycle of work on the use of tiling for packaging in

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29

Zhao, Jiaxin. "Coverage Path Planning with Adaptive Hyperbolic Grid for Step-Stare Imaging System." Drones 8, no. 6 (2024): 242. http://dx.doi.org/10.3390/drones8060242.

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Step-stare imaging systems are widely used in aerospace optical remote sensing. In order to achieve fast scanning of the target region, efficient coverage path planning (CPP) is a key challenge. However, traditional CPP methods are mostly designed for fixed cameras and disregard the irregular shape of the sensor’s projection caused by the step-stare rotational motion. To address this problem, this paper proposes an efficient, seamless CPP method with an adaptive hyperbolic grid. First, we convert the coverage problem in Euclidean space to a tiling problem in spherical space. A spherical approx

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30

Avelino, Catarina P., and Altino F. Santos. "Spherical F-Tilings by Triangles and $r$-Sided Regular Polygons, $r \ge 5$." Electronic Journal of Combinatorics 15, no. 1 (2008). http://dx.doi.org/10.37236/746.

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The study of dihedral f-tilings of the sphere $S^2$ by spherical triangles and equiangular spherical quadrangles (which includes the case of 4-sided regular polygons) was presented by Breda and Santos [Beiträge zur Algebra und Geometrie, 45 (2004), 447–461]. Also, in a subsequent paper, the study of dihedral f-tilings of $S^2$ whose prototiles are an equilateral triangle (a 3-sided regular polygon) and an isosceles triangle was described (we believe that the analysis considering scalene triangles as the prototiles will lead to a wide family of f-tilings). In this paper we extend these results,

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31

Avelino, Catarina P., and Altino F. Santos. "Spherical f-Tilings by Scalene Triangles and Isosceles Trapezoids III." Electronic Journal of Combinatorics 16, no. 1 (2009). http://dx.doi.org/10.37236/176.

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The study of the dihedral f-tilings of the sphere $S^2$ whose prototiles are a scalene triangle and an isosceles trapezoid was initiated in parts I and II. In this paper we complete this classification presenting the study of all dihedral spherical f-tilings by scalene triangles and isosceles trapezoids in the remaining case of adjacency. A list containing all the f-tilings obtained in this paper is presented. It is composed by isolated tilings as well as discrete and continuous families of tilings. The combinatorial structure is also achieved.

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32

Huson, DanielH. "Ribbon tilings from spherical ones." Geometriae Dedicata 63, no. 2 (1996). http://dx.doi.org/10.1007/bf00148214.

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33

Breda, Ana, and Altino F. Santos. "Dihedral f-tilings of the sphere by rhombi and triangles." Discrete Mathematics & Theoretical Computer Science Vol. 7 (January 1, 2005). http://dx.doi.org/10.46298/dmtcs.348.

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International audience We classify, up to an isomorphism, the class of all dihedral f-tilings of S^2, whose prototiles are a spherical triangle and a spherical rhombus. The equiangular case was considered and classified in Ana M. Breda and Altino F. Santos, Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles. Here we complete the classification considering the case of non-equiangular rhombi.

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34

Breda, A. M. d'Azevedo, Patrícia S. Ribeiro, and Altino F. Santos. "Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles - II." Electronic Journal of Combinatorics 15, no. 1 (2008). http://dx.doi.org/10.37236/815.

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The study of dihedral f-tilings of the Euclidean sphere $S^2$ by triangles and $r$-sided regular polygons was initiated in 2004 where the case $r=4$ was considered [5]. In a subsequent paper [1], the study of all spherical f-tilings by triangles and $r$-sided regular polygons, for any $r\ge 5$, was described. Later on, in [3], the classification of all f-tilings of $S^2$ whose prototiles are an equilateral triangle and an isosceles triangle is obtained. The algebraic and combinatorial description of spherical f-tilings by equilateral triangles and scalene triangles of angles $\beta$, $\gamma$

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35

Gdawiec, Krzysztof, Kwok Wai Chung, Alain Nicolas, David Bailey, and Peichang Ouyang. "Visualization of Escher‐like Kaleidoscopic Spherical Patterns of Regular Polyhedron Symmetry." Computer Graphics Forum, January 3, 2024. http://dx.doi.org/10.1111/cgf.14999.

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AbstractIn this paper, we present a method for creating Escher‐like spherical patterns with regular polyhedron symmetries. Using the generators of the symmetry groups associated with regular polyhedra, we first provide fast algorithms to construct spherical tilings. Then, to obtain Escher‐like patterns, we specify texturing techniques to decorate the resulting tilings. Moreover, we present a strategy to create a novel dynamic effect of Escher‐like kaleidoscopes in which the motifs have a complete body. The method has the advantages of simple implementation, fast calculation, good graphics, and

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36

Breda, A. M. d'Azevedo, Patrícia S. Ribeiro, and Altino F. Santos. "Dihedral f-Tilings of the Sphere by Equilateral and Scalene Triangles - III." Electronic Journal of Combinatorics 15, no. 1 (2008). http://dx.doi.org/10.37236/871.

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The study of spherical dihedral f-tilings by equilateral and isosceles triangles was introduced in [3]. Taking as prototiles equilateral and scalene triangles, we are faced with three possible ways of adjacency. In [4] and [5] two of these possibilities were studied. Here, we complete this study, describing the f-tilings related to the remaining case of adjacency, including their symmetry groups. A table summarizing the results concerning all dihedral f-tilings by equilateral and scalene triangles is given in Table 2.

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37

T�th, L. Fejes. "On spherical tilings generated by great circles." Geometriae Dedicata 23, no. 1 (1987). http://dx.doi.org/10.1007/bf00147392.

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38

Dawson, Robert J. MacG, and Blair Doyle. "Tilings of the Sphere with Right Triangles I: The Asymptotically Right Families." Electronic Journal of Combinatorics 13, no. 1 (2006). http://dx.doi.org/10.37236/1074.

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Sommerville and Davies classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper determines which right spherical triangles within certain families can tile the sphere.

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39

Dawson, Robert J. MacG, and Blair Doyle. "Tilings of the Sphere with Right Triangles II: The $(1,3,2)$, $(0,2,n)$ Subfamily." Electronic Journal of Combinatorics 13, no. 1 (2006). http://dx.doi.org/10.37236/1075.

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Sommerville and Davies classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper shows that no right triangles in a certain subfamily can tile the sphere, although multilayered tilings are possible.

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40

Dawson, Robert J. MacG, and Blair Doyle. "Tilings of the sphere with right triangles III: the asymptotically obtuse families." Electronic Journal of Combinatorics 14, no. 1 (2007). http://dx.doi.org/10.37236/966.

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Sommerville and Davies classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. However, if the edge-to-edge restriction is relaxed, there are other such triangles; here, we continue the classification of right triangles with this property begun in our earlier papers. We consider six families of triangles classified as "asymptotically obtuse", and show that they contain two non-edge-to-edge tiles, one (with angles of $90^\circ$, $105^\circ$ and $45^\circ)$ believed to be previously unknown.

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41

Avelino, Catarina P., and Altino F. Santos. "Triangular spherical dihedral f-tilings: the $(\pi/2, \pi/3, \pi/4)$ and $(2\pi/3, \pi/4, \pi/4)$ family." Revista de la Unión Matemática Argentina, December 11, 2020, 367–87. http://dx.doi.org/10.33044/revuma.v61n2a12.

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42

Durn, James, and Alireza Behnejad. "Application of Aperiodic Tiling to Lattice Spatial Structures." Symmetry: Art and Science | 12th SIS-Symmetry Congress, 2022, 138–46. http://dx.doi.org/10.24840/1447-607x/2022/12-17-138.

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The aim of this report is to expand on the existing available configurations for lattice spa- tial structures and in turn widen the range of design options that can be presented to architects and/or clients. This is achieved by developing a new family of configurations in which the aperiodic tiling pattern ‘Penrose Kite and Dart’ tiling is applied to spherical caps using formex configuration pro- cessing techniques. To further expand this new family, the pattern modification of triangulation is suggested along with alternative projection methods of changing the shape of the initial tiling patc

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43

Staub, Mark C., Shichen Yu, and Christopher Y. Li. "Poly (3‐hexylthiophene) (P3HT) Crystalsomes: Tiling 1D Polymer Crystals on a Spherical Surface." Macromolecular Rapid Communications, July 25, 2022, 2200529. http://dx.doi.org/10.1002/marc.202200529.

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44

Toyooka, Ryuya, Seri Nishimoto, Tomoya Tendo, Takashi Horiyama, Tomohiro Tachi, and Yasuhiro Matsunaga. "Explicit description of viral capsid subunit shapes by unfolding dihedrons." Communications Biology 7, no. 1 (2024). http://dx.doi.org/10.1038/s42003-024-07218-x.

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AbstractViral capsid assembly and the design of capsid-based nanocontainers critically depend on understanding the shapes and interfaces of constituent protein subunits. However, a comprehensive framework for characterizing these features is still lacking. Here, we introduce a novel approach based on spherical tiling theory that explicitly describes the 2D shapes and interfaces of subunits in icosahedral capsids. Our method unfolds spherical dihedrons defined by icosahedral symmetry axes, enabling systematic characterization of all possible subunit geometries. Applying this framework to real T

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45

Cao, Yu, Alexander Scholte, Marko Prehm, et al. "Understanding the Role of Trapezoids in Honeycomb Self‐Assembly – Pathways between a Columnar Liquid Quasicrystal and its Liquid‐Crystalline Approximants." Angewandte Chemie International Edition, November 27, 2023. http://dx.doi.org/10.1002/anie.202314454.

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Quasiperiodic patterns and crystals ‐ having long range order without translational symmetry ‐ fascinate researchers since their discovery. In this study, we report on new p‐terphenyl based T‐shaped facial polyphiles with two alkyl end‐chains and a glycerol‐based hydrogen‐bonded side‐group, self‐assembling into an aperiodic columnar liquid quasicrystal with 12‐fold symmetry and its periodic liquid‐crystalline approximants with complex superstructures. All represent honeycombs formed by self‐assembly of the p‐terphenyls, dividing space into prismatic cells with polygonal cross‐sections. In the

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46

Cao, Yu, Alexander Scholte, Marko Prehm, et al. "Understanding the Role of Trapezoids in Honeycomb Self‐Assembly – Pathways between a Columnar Liquid Quasicrystal and its Liquid‐Crystalline Approximants." Angewandte Chemie, November 27, 2023. http://dx.doi.org/10.1002/ange.202314454.

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Quasiperiodic patterns and crystals ‐ having long range order without translational symmetry ‐ fascinate researchers since their discovery. In this study, we report on new p‐terphenyl based T‐shaped facial polyphiles with two alkyl end‐chains and a glycerol‐based hydrogen‐bonded side‐group, self‐assembling into an aperiodic columnar liquid quasicrystal with 12‐fold symmetry and its periodic liquid‐crystalline approximants with complex superstructures. All represent honeycombs formed by self‐assembly of the p‐terphenyls, dividing space into prismatic cells with polygonal cross‐sections. In the

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47

Eppstein, David. "On Polyhedral Realization with Isosceles Triangles." Graphs and Combinatorics, April 11, 2021. http://dx.doi.org/10.1007/s00373-021-02314-9.

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AbstractAnswering a question posed by Joseph Malkevitch, we prove that there exists a polyhedral graph, with triangular faces, such that every realization of it as the graph of a convex polyhedron includes at least one face that is a scalene triangle. Our construction is based on Kleetopes, and shows that there exists an integer i such that all convex i-iterated Kleetopes have a scalene face. However, we also show that all Kleetopes of triangulated polyhedral graphs have non-convex non-self-crossing realizations in which all faces are isosceles. We answer another question of Malkevitch by obse

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48

Lin, Hong Sheng, and Yu Jian Cheng. "A Tiling Method for Sub-Arrayed Spherical Conformal Phased Array Antennas Based on Maximum 3-Dimensional Space Entropy Model." IEEE Transactions on Antennas and Propagation, 2024, 1. http://dx.doi.org/10.1109/tap.2024.3359850.

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49

Rochal, Sergei B., Aleksey S. Roshal, Olga V. Konevtsova, and Rudolf Podgornik. "Proteinaceous Nanoshells with Quasicrystalline Local Order." Physical Review X 14, no. 3 (2024). http://dx.doi.org/10.1103/physrevx.14.031019.

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Among various proteinaceous nanocontainers and nanoparticles, the most promising ones for various applications in nano- and medical science appear to be those whose structures differ fundamentally from icosahedral viral capsids described by the paradigmatic Caspar-Klug model. By analyzing such anomalous assemblies represented in the Protein Data Bank, we identify a series of shells with square-triangular local order and find that most of them originate from short-period approximants of a dodecagonal tiling consisting of square and triangular tiles. Examining the nonequilibrium assembly of such

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50

Achilleos, Andrea, James Hardwick, Ryuji Hirayama, and Sriram Subramanian. "Omnidirectional Transmissive Acoustic Metasurfaces Based on Goldberg Polyhedra." Advanced Functional Materials, April 29, 2025. https://doi.org/10.1002/adfm.202502899.

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AbstractAcoustic metasurfaces (AMs) are engineered structures that control acoustic wave propagation, enabling applications such as sound absorption, beam steering, and acoustic holography. Most AMs are planar and operate in a single direction, limiting the spatial extent of target acoustic fields. The simultaneous manipulation of waves in multiple directions remains largely unexplored, and omnidirectional AMs have yet to be realized. This study introduces a design and fabrication approach for omnidirectional AMs capable of generating custom acoustic fields anywhere in 3D space. Inspired by Go

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