Triakis Solids and Harmonic Functions
Miki Hasui, Katsunori Iwasaki
TL;DR
This paper explores harmonic functions on specific triakis solids, revealing that polyhedral harmonics can surpass group harmonics, which is a novel discovery in the study of harmonic functions on polyhedra.
Contribution
It provides the first examples where polyhedral harmonic functions are strictly larger than group harmonic functions for certain triakis solids.
Findings
Polyhedral harmonics exceed group harmonics in these solids.
First known examples demonstrating this strict inequality.
Advances understanding of harmonic functions on polyhedral structures.
Abstract
We describe the harmonic functions for certain isohedral triakis solids. They are the first examples for which polyhedral harmonics is strictly larger than group harmonics.
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
TopicsSpectral Theory in Mathematical Physics · Quasicrystal Structures and Properties · Mathematical functions and polynomials