Conjugate-dual clusters
Silei Wang, Jing Tian, Jiayu Li, Tian Gong, Xing Yan, Jijun Zhao and, Xin-Gao Gong, Xiao Gu

TL;DR
This paper introduces a systematic method for discovering high-symmetry clusters using conjugate-dual structures, combining polyhedra and their duals to generate new stable cluster families.
Contribution
It proposes the novel conjugate-dual (co-dual) concept to systematically construct high-symmetry clusters, expanding the exploration of symmetrical polyhedral structures.
Findings
Identified stable cage-like and core-shell co-dual clusters.
Developed a systematic approach to explore high symmetrical structures.
Discovered new families of high symmetrical clusters.
Abstract
Discovery of clusters with high symmetrical geometry, such as C60 fullerene, always attract lots of interest because of their diverse nature. However, most of such interesting cluster were sporadically discovered, is there any systematic method to explore all possible high symmetrical clusters? Herein, we propose an idea to systematically construct high symmetrical structures based on novel conjugate-dual (co-dual) concept. A co-dual structure would be constructed by conjugately combining one high symmetrical polyhedron and its corresponding dual. In such co-dual structures, the symmetry of the original polyhedron could be kept or even promoted in some special cases. This provides a way to explore high symmetrical polyhedra and leads to a new cluster family, co-dual clusters. In this paper, we have systematically studied the spherical co-dual clusters with one- or two-element shells,…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic
