Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part i

Filipe A. Dos Santos, Antonino Favata, Andrea Micheletti, Roberto Paroni, Marco Picchi Scardaoni

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The control of the shape of complex metasurfaces is a challenging task often addressed in the literature. This work presents a class of tessellated plates able to deform into surfaces of preprogrammed shape upon activation by any flexural load and that can be controlled by a single actuator. Quadric metasurfaces are obtained from infinitesimal origami maps of monohedral hexagonal tessellations of the plane, that is pavings in which all tiles are congruent to each other. Monohedral tessellated portions can be joined together to obtain more complex shapes, which can be locally synclastic or anticlastic and can have a certain roughness. We broaden previous work by providing a complete characterization of all the three known types of monohedral tessellations composed by irregular hexagons. The proposed two-dimensional structures may have applications in prosthetics, tissue engineering, wearable devices, energy harvesting devices, tunable focus mirrors and adaptive facades. The study is divided in two parts. In Part I, after introducing the discrete kinematics of tessellated plates, it is proved analytically that essentially each type of monohedral hexagonal tessellation possesses only one deformation mode. Afterwards, several numerical examples are provided to demonstrate the variety of achievable surface shapes. In Part II, first the metasurfaces corresponding to assigned tile geometries are given a continuum description, which establishes that the continuous interpolant is always a quadric. Then, experimental results on fabrication, assembly and surface accuracy are reported.
Original languageEnglish
Article number20230430
Number of pages20
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2283
Publication statusPublished - 14 Feb 2024


  • 3D-printing
  • metasurface
  • morphing structure
  • rigid microstructure
  • tessellation


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