Divided Spheres presents six classic techniques for subdividing a sphere. Each technique subdivides a principle triangle of a spherical polyhedra and results in a set of points on the sphere. When neighboring points are connected with chords or arcs, an even triangulated grid forms over the principle triangle. To cover the entire sphere without overlaps or gaps, this set of points are copied and rotated to other positions on the sphere’s surface. Divided Spheres explains how this is done. You can download the points for the principle triangle of a spherical icosahedron and experiment with them in a variety of display programs. You can also manipulate or edit them to create your own design patterns by connecting the points in different layouts.

To download a set of grid coordinates, orientation figure or grid point numbering schema, just click on the subdivision schema you are interested in. All coordinate sets are for the principle triangle of a spherical icosahedron with a frequency 8 grid:

Class I Grid SchemasDivided Spheres Front Cover

Class II Grid SchemaDivided Spheres Front Cover

Class III Grid SchemaDivided Spheres Front Cover



Creative Commons License
Divided Spheres schema grid coordinates by Edward S. Popko is licensed under a Creative Commons Attribution 3.0 Unported License. Based on a work at dividedspheres.com.