Symmetric diagrams for all strongly invertible knots up to 10 crossings

TL;DR

This paper provides a comprehensive table of symmetric diagrams for strongly invertible knots up to 10 crossings, highlighting similarities with symmetric union diagrams and discussing open questions in the field.

Contribution

It introduces a complete catalog of symmetric diagrams for these knots and explores their relation to symmetric union diagrams, advancing understanding of knot symmetry.

Findings

Table of symmetric diagrams for knots up to 10 crossings

Similarity between transvergent and symmetric union diagrams

Discussion of open questions in knot symmetry

Abstract

We present a table of symmetric diagrams for strongly invertible knots up to 10 crossings, point out the similarity of transvergent diagrams for strongly invertible knots with symmetric union diagrams and discuss open questions.