A new method for generalizing non-self-intersecting flexible polyhedra
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918191412805632 |
|---|---|
| author | He, Zeyuan Guest, Simon D. |
| author_facet | He, Zeyuan Guest, Simon D. |
| contents | A surface is considered flexible if it allows a continuous deformation that preserves both metric and smoothness. We introduce a novel construction method, called 'base + crinkle,' for generating a broad class of non-self-intersecting flexible closed polyhedral surfaces (i.e. flexible polyhedra). These flexible polyhedra can be non-triangulated, exhibit multiple kinematic degrees of freedom, and possess topologies beyond the sphere. The geometric result provides fresh insights into the geometry of origami and the design of engineering mechanisms, such as sealed-chamber robotics and distortion-free metamorphic grippers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new method for generalizing non-self-intersecting flexible polyhedra He, Zeyuan Guest, Simon D. Metric Geometry A surface is considered flexible if it allows a continuous deformation that preserves both metric and smoothness. We introduce a novel construction method, called 'base + crinkle,' for generating a broad class of non-self-intersecting flexible closed polyhedral surfaces (i.e. flexible polyhedra). These flexible polyhedra can be non-triangulated, exhibit multiple kinematic degrees of freedom, and possess topologies beyond the sphere. The geometric result provides fresh insights into the geometry of origami and the design of engineering mechanisms, such as sealed-chamber robotics and distortion-free metamorphic grippers. |
| title | A new method for generalizing non-self-intersecting flexible polyhedra |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2505.05629 |