All the spherical imagery in Chapter 10 of the second edition of Divided Spheres was generated with DisplaySphere, a program specially developed by Chris Kitrick to render and capture spherical geometry utilizing graphics hardware typically available on today’s computers. It is specifically designed to minimize the amount of geometric data required to build spherical frameworks based on the platonic solids. It has many features that are useful for visualizing and understanding spherical structures.

DisplaySphere is designed to import industry standard OFF (Object File Format) geometry files and provides a plethora of options to augment the visual aspects of the geometry, including faces, edges, and vertices. Features include stereo rendering. Geometric data is analyzed during import to determine uniqueness that can be displayed numerically through automatic color assignment. The software is freely available through GitHub and includes full documentation in PDF format along with sample geometry including the ones used in Chapter 10.


From the documentation:

DisplaySphere is a Windows application specifically enhanced for viewing spherical geometry. It uses the OpenGL API for rendering geometry and is optimized for four platonic polyhedra: the icosahedron, octahedron, cube, and tetrahedron. For these polyhedra only the definition of one face, or a symmetrical subset of the entire polyhedron, is required since the rest of the polyhedron can be constructed from rotational duplicates of the single face. Though optimized for spherical geometry the program will display non‐spherical geometry with all the same controls available.

The application will allow basic viewing control of one or more geometries that can be inputted in multiple formats and allow topological components to be viewed separately or simultaneously; such as faces, edges, and vertices. Edges and vertices are constructed from face information with multiple variations available for form, size, and color. In addition, there is support for image capture both in single and multiple frames. The size of the render, and the colors used are user selectable. More
advanced rendering features allow for orthographic and stereo projection.

Utilization of hardware‐based rendering, using the OpenGL API, allows efficient real time rendering of the geometry. The application also uses multi‐sampling per pixel to achieve a relatively high level of image quality.