Platonic Dynamics

Perfect $2$-colorings of the Platonic graphs

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

Constructing Finite Frames via Platonic Solids

Finite tight frames have many applications and some interesting physical interpretations. One of the important subjects in this area is the ways for constructing such frames. In this article we give a concrete method for constructing finite normalized frames using Platonic solids.

Sadr-ul-Muta'allehin on Platonic Ideas

Sadr-ul-Muta'allehin on Platonic Ideas

Excited Platonic Sphalerons in the Presence of a Dilaton Field

We construct sphaleron solutions with discrete symmetries in Yang-Mills-Higgs theory coupled to a dilaton. These platonic sphalerons are related to rational maps of degree N . We demonstrate that, in the presence of a dilaton, for a given rational map excited platonic sphalerons exist beside the fundamental platonic sphalerons. We focus on platonic sphaleron solutions with N = 4, which possess ...