Related papers: Rigid foldability of the augmented square twist
Kirigami-inspired designs can enable self-folding three-dimensional materials from flat, two-dimensional sheets. Hierarchical designs of connected levels increase the diversity of possible target structures, yet they can lead to longer…
This note is devoted to a special Fano fourfold defined by a four-dimensional space of skew-symmetric forms in five variables. This fourfold appears to be closely related with the classical Segre cubic and its Cremona-Richmond configuration…
We relate the stability of knot invariants under twisting a pair of strands to the stability of symmetric quivers under unlinking (or linking) operation. Starting from the HOMFLY-PT skein relations, we confirm the stable growth of…
A rectangle in the plane can be continuously deformed preserving its edge lengths, but adding a diagonal brace prevents such a deformation. Bolker and Crapo characterized combinatorially which choices of braces make a grid of squares…
An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a *net*, a connected planar piece with no overlaps. A *grid unfolding* allows additional cuts along grid edges induced by coordinate planes…
A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and preserving the topology of the surface. A complete list of…
Plates generally admit six deformation modes: three of which are high in strain energy, stretch the plate's midsurface and are called membrane modes; and three are low-energy, bend the midsurface without stretching it and are called bending…
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual…
In this paper, we investigate the properties of well-rounded twists of a given ideal lattice of an imaginary quadratic field $K$. We show that every ideal lattice $I$ of $K$ has at least one well-rounded twist lattice. Moreover, we provide…
Existing Civil Engineering structures have limited capability to adapt their configurations for new functions, non-stationary environments, or future reuse. Although origami principles provide capabilities of dense packaging and…
We propose a novel computational framework for modeling and simulating origami structures. In this framework, bilinear solid-shell elements are employed to model the origami panels while crease folding is considered through the angle…
A new continuous model of shearable rod, subject to large elastic deformation, is derived from nonlinear homogenization of a one-dimensional periodic microstructured chain. As particular cases, the governing equations reduce to the Euler…
Single-mode deformations of two-dimensional materials, such as the Miura-ori zig-zag fold, are important to the design of deployable structures because of their robustness; these usually require careful pre-patterning of the material. Here…
The article studies the elastic and locomotive properties of Miura-ori-type paper origami. The mechanics of a single paper crease is studied experimentally, and its non-elastic properties turn out to be crucial. The entire origami…
A countable structure is said to be extendible if it has the same Scott sentence as some uncountable structure. Rigid structures are not extendible. We give an example of an extendible model with a rigid elementary extension.
Origami designs and structures have been widely used in many fields, such as morphing structures, robotics, and metamaterials. However, the design and fabrication of origami structures rely on human experiences and skills, which are both…
Gupta et al. [1, 2] describe a very beautiful application of algebraic geometry to lattice structures composed of quadric of revolution (quador) implicit surfaces. However, the shapes created have concave edges where the stubs meet, and…
Kirigami-inspired metamaterials are attracting increasing interest because of their ability to achieve extremely large strains and shape changes via out-of-plane buckling. While in flat kirigami sheets the ligaments buckle simultaneously as…
We present a general deconstruction procedure aimed at recognizing whether a given conformal model may be obtained as an orbifold of another one, and to identify the twist group and the original model in terms of some readily available…
Reconfigurable mechanical systems enable precise programmable control over structural properties, opening new opportunities in architected materials, adaptive devices, and multifunctional structures. Here, we introduce elastic rod origami…