Geometric classification of real ternary octahedral quartics

TL;DR

This paper classifies real ternary quartic surfaces with octahedral symmetry, revealing a new type of surface that expands understanding of symmetric quartic geometries.

Contribution

It provides a comprehensive geometric classification of octahedral symmetric quartic surfaces, introducing a novel surface type not previously documented.

Findings

Classification of octahedral symmetric quartics completed

Discovery of a new surface type within this class

Enhanced understanding of symmetric quartic geometries

Abstract

Ternary real-valued quartics in $\mathbb{R}^3$ being invariant under octahedral symmetry are considered. The geometric classification of these surfaces is given. A new type of surfaces emerge from this classification.