The program allows you to create an unlimited number of tessellations by selecting “File -> New” from the menu.
When viewing a tessellation, click-and-drag inside of it to shift its position within hyperbolic space. You can also click-and drag with the right mouse button to manipulate the truncation of the tessellation.
The “Tessellation Controls” window allows you to change the settings for the tessellation that is currently active.
# p and q — The numbers specified by p and q refer to the Schläfli symbol {p,q} of the tessellation. The Schläfli symbol is a simple way of classifying tessellations where p is the number of sides in each polygon, and q is the number of polygons that meet at each vertex.
# Max. Vertices — This specifies the number of vertices that will be drawn (how far the tessellation will extend towards the disk boundary). More vertices will take exponentially longer to draw. Also, with more vertices, clicking-and-dragging the tessellation will become slower. With a good screen resolution, 10000 vertices fills up the Poincaré disk almost completely.
# Model — Select “Poincaré” to draw the tessellation on a Poincaré-style disk, and “Klein” to draw on a Klein-style disk. The Klein disk is Similar to the Poincaré disk, except the Klein disk transforms hyperbolic space so that a line Between two points appears as a straight line, instead of a Circle arc, which is what the Poincaré disk gives.
# Quality — Select “Low” to display simple straight lines between vertices (and let the tessellation be drawn much FASTER). Select “High” to draw actual curved lines between vertices. This will slow down drawing considerably.
# Truncation — This is a list of predefined levels of truncation for the tessellation. Select from this list to apply a certain truncation. You can also do free-form truncation by clicking-and-dragging on the tessellation with the right mouse button.
