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Triangulation of surfaces. Any curved surface, in this case a sphere, can be approximated by a mesh of triangles in a process called triangulation. A larger mesh of triangular faces gives a better approximation of the original surface. Shown are polyhedral triangulations of a sphere with n triangular faces

Triangulation of surfaces. Any curved surface, in this case a sphere, can be approximated by a mesh of triangles in a process called triangulation. A larger mesh of triangular faces gives a better approximation of the original surface. Shown are polyhedral triangulations of a sphere with n triangular faces

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Dilational structures can change in size without changing their shape. Current dilational designs are only suitable for specific shapes or curvatures and often require parts of the structure to move perpendicular to the dilational surface, thereby occupying part of the enclosed volume. Here, we present a general method for creating dilational struc...

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... The first step of the presented design method is to triangulate the curved surface from which we want to create a dilational structure. Triangulation is a common strategy to approximate curved surfaces by a mesh of triangular faces and lies at the basis of the STL file format used in 3D printing 22,23 . Triangulation is illustrated in Fig. 2 for a sphere. It is observed that the accuracy of the approximation increases with the number of triangular faces in the resulting ...

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... On the one side of the spectrum, mechanical metamaterials [1][2][3] are rationally designed to exhibit exotic material-like properties, such as negative effective values of the Poisson's ratio [4][5][6] , thermal expansion [7][8][9] , and stiffness 10,11 . On the other side of the spectrum, however, one finds such concepts as mechanical logic gates 12,13 , adaptive-stiffness mechanisms 14,15 , and shape-shifting designs [16][17][18][19] , which exhibit device-like functionalities. As opposed to traditional machines, which are usually highly dynamic, the vast majority of the mechanical metamaterials designed to date work quasi-statically. ...
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