Sculptures in S^3

TL;DR

This paper presents the creation of geometric sculptures inspired by designs on the three-dimensional sphere, transferred to Euclidean space via stereographic projection and fabricated using 3D printing.

Contribution

It introduces a method to design and produce sculptures based on spherical geometry and stereographic projection, combining mathematical visualization with modern fabrication.

Findings

Successful transfer of spherical designs to Euclidean space

Fabrication of sculptures using 3D printing technology

Visualization of complex spherical geometries in physical form

Abstract

We construct a number of sculptures, each based on a geometric design native to the three-dimensional sphere. Using stereographic projection we transfer the design from the three-sphere to ordinary Euclidean space. All of the sculptures are then fabricated by the 3D printing service Shapeways.