Abstract
Mathematics teachers, artists using mathematical symmetry in their work, and curious mathematicians can benefit
from becoming familiar with John Conway’s unifying work on symmetry. Conway expanded on William
Thurston’s concept of orbifolds by developing a set of notations, along with an accounting system for them called
“cost,” which allows simple arithmetic to be used to determine what types of patterns are possible. Conway and
Thurston described many types of spaces, but we will focus only on patterns in the plane. Conway presents
orbifolds as objects made by repeatedly folding patterns onto themselves until there is just one copy of a
fundamental region. This workshop will provide hands-on experience with the orbifold signatures and calculating
the cost of a pattern. We will introduce tools for designing patterns and build physical orbifolds from specific
patterns.
