3d-printing Identification Spaces of the Square

TL;DR

This paper explores three different ways to identify edges of a square, presents interesting 3D immersions of these spaces, and provides methods to create 3D-printable models of their parametrizations.

Contribution

It introduces new identification spaces of the square, details their immersions into 3D, and offers a process for constructing printable models of these spaces.

Findings

Three identification spaces of the square are described.

Methods for constructing 3D-printable models are provided.

The paper demonstrates interesting immersions into D space.

Abstract

We describe three identification spaces of the square, interesting choices of immersion into $\mathbb{R}^3$, and a process to construct 3d-printable models of their parametrizations.