# An existence result on two-orbit maniplexes

## TL;DR

This paper proves that for 2-orbit maniplexes, the symmetry type graphs satisfying certain properties are always realizable as the symmetry type graph of some 2-orbit maniplex, extending understanding of maniplex symmetry structures.

## Contribution

It provides a complete existence result for 2-orbit maniplexes, showing that any suitable symmetry type graph corresponds to an actual maniplex.

## Key findings

- All 2-orbit symmetry type graphs satisfying the specific properties are realizable.
- The result extends the classification of maniplexes with two symmetry orbits.
- Provides a foundation for exploring higher orbit maniplexes.

## Abstract

A maniplex of rank n is a connected, n-valent, edge-coloured graph that generalises abstract polytopes and maps. If the automorphism group of a maniplex M partitions the vertex-set of M into k distinct orbits, we say that M is a k-orbit n-maniplex. The symmetry type graph of M is the quotient pregraph obtained by contracting every orbit into a single vertex. Symmetry type graphs of maniplexes satisfy a series of very specific properties. The question arises whether any pregraph of order k satisfying these properties is the symmetry type graph of some k-orbit maniplex. We answer the question when k = 2.