Non-orientable surfaces in 4-dimensional space

TL;DR

This survey paper explores the detailed constructions and visualizations of non-orientable surfaces embedded and immersed in 4-dimensional space, emphasizing their projections into 3D and 2D for illustration.

Contribution

It provides comprehensive constructions and illustrations of non-orientable surfaces in 4D, including methods for their visualization through successive projections.

Findings

Detailed constructions of non-orientable surfaces in 4D

Illustrations based on projections into 3D and 2D

Development of concepts for visualizing complex surfaces

Abstract

This article is a survey article that gives detailed constructions and illustrations of some of the standard examples of non-orientable surfaces that are embedded and immersed in 4-dimensional space. The illustrations depend upon their 3-dimensional projections, and indeed the illustrations here depend upon a further projection into the plane of the page. The concepts used to develop the illustrations will be developed herein.