'Escher' Sphere Tiler

This program allows you to create symmetrically tiled patterns on a sphere, similar to the tilings of the plane and other geometries by MC Escher.

SphereTiler.exe - Windows OpenGL executeable.

Lizard (raised)
Beveled Dodecahedron
Point Swirl
Snub Dodecahedron
Swirly 2
Truncated Dodecahedron
Color Weave


When you first load up the program, it displays a blank sphere with some purple dots. The purple dots are special points that do not move when you apply the symmetric rotations (by default, the program starts using the standard dodecahedral/icosahedral symmetry). I'll go into more detail on those later. Meanwhile, notice when you move your mouse over the sphere, the cursor point appears as a red dot, with a red line coming out of it. The red line always points straight out of the sphere (i.e. along the normal).


To rotate the sphere, press and hold the right mouse button. To zoom, press the shift key while moving the mouse up and down.

Creating points

To create a point, hold shift and click the left mouse button. A point will be created at that location on the sphere. Furthermore, all the symmetric points will be created simultaneously.

To select and drag a point, use the left mouse button without the shift key. As you move a point around, all the symmetric points move as well. Playing around with this a little, you will notice that as you drag a point near to one of the purple dots, all of it's symmetric points also converge on the purple dots. Some of the purple dots have 5-fold symmetry - that is, 5 symmetric dots will converge on that dot simultaneously - while others have 2 or 3-fold symmetry.

5-fold symmetry

To create a second point, shift-left click near to the first point. If the first point was still selected, the second point should now be connected to the first by a line. In general, a new point will automatically be connected to the selected point, and will become the new selected point. This allows you to sketch curves quickly.

Sketching a curve by holding shift and left-clicking.

You can select existing points by left-clicking them. If you wish to create a new point that is not connected to any existing points, you must deselect all points. To deselect, simply left-click anywhere but on a point.

To delete a point, select it and hit the delete key.

Gluing Points

Two existing points can be combined, or 'glued' together. To do this, select the first point, hit the 'g' key, and left-click the second point. They will merge to a single point, maintaining all of the line connections. The position of the new point will in general be the position of the second point. Note, however, that if you glue a point to one of it's symmetric points, it will collapse to the nearest purple point. This is because a point cannot be symmetric with itself, UNLESS it is at a purple point.

Gluing a point to a symmetric point results in it collapsing to a purple point.

Creating faces

I need to write this section still. But, in short, Select a point and press 'c'. Selecting the point so that the correct side is filled in is a little more complicated than that, but I'll have to explain it later.