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The gyroid lattice is prepared in chiral and non‐chiral forms. The chiral gyroid lattice is observed to exhibit temperature‐induced twist with the direction of twist corresponding to the sense of chirality. This effect is a nonclassical effect that cannot occur in classical elasticity or classical thermo‐elasticity but is allowable in Cosserat solids. Poisson's ratio of the gyroid is known to be about 0.3 with minimal dependence on size. In contrast to squeeze–twist coupling in which substantial size effects occur with slender specimens twisting much more than thicker ones, thermal–twist coupling exhibits opposite and less consistent size effects of much smaller magnitude.
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Quasi-twisting convex polyhedra
We introduce a notion we call quasi-twisting that cuts a convex polyhedron P into two halves and reglues the halves to form a different convex polyhedron. The cut is along a simple closed quasigeodesic. We initiate the study of the range of polyhedra produced by quasi-twisting P, and in particular, whether P can “quasi-twist flat,” i.e., produce a flat, doubly-covered polygon. We establish a sufficient condition and some necessary conditions, which allow us to show that of the five Platonic solids, the tetrahedron, cube, and oc- tahedron can quasi-twist flat. We conjecture that the dodecahedron and icosahedron cannot quasi-twist flat, and prove that they cannot under certain restrictions. Many open problems remain.
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- PAR ID:
- 10418536
- Editor(s):
- Bahoo, Y.; Georgiou, K.
- Date Published:
- Journal Name:
- Proc. of the 34th Canadian Conference on Computational Geometry (CCCG 2022)
- Page Range / eLocation ID:
- 270-276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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