Topology

Topology has quite a complex meaning and is a major area in both mathematics and sculpting. Topology is essentially the way in which you can redefine a shape through deformations that include stretching, but not tearing or gluing. This is similar to the core mechanic of how ZBrush and Mudbox work, and Topology can be very useful to keep in mind when finishing a sculpture.

When you create a digital sculpture in either ZBrush of Mudbox, the resolution and sub-division is normally very high to accommodate all the detail present. ZBrush converts the on-screen polygon level into their own specific display format called 'Pixols', whereas Mudbox presents the polygons essentially as they appear in the render view. The difference this makes is that ZBrush generally runs a lot faster, and you can achieve higher levels of sub-division on less powerful machines, however sculptures that you create in Mudbox are essentially what-you-see-is-what-you-get, unlike ZBrush who's rendering can often display graphical glitches not present in the draft view. Because of this, models creating in ZBrush and Mudbox need to be reduced in polygons without losing detail, which has to be done in a very efficient process to maximize the amount of polygons saved. It is also essential that the muscles in the face are all in the correct position, otherwise when animating the muslces in the face won't behave as they should (stretch), and instead the muscles will appear to 'tear'. This is where Topology comes in handy.

Topology can be used to calculate the most efficient way to recreate a model. By following the muscles in Facial Topology, you can more accurate reconstruct a face while minimising quality loss. The Facial Topology i used for my sculpt can be found here: http://www.foundation3d.com/gallery/showphoto.php/photo/430/cat/500/ppuser/4

http://en.wikipedia.org/wiki/Topology
http://www.pixologic.com/home.php
http://usa.autodesk.com/adsk/servlet/pc/index?id=13565063&siteID=123112