Iris folding is an art-form consisting of layered strips of paper, forming a spiral pattern behind an aperture, which can be used to make cards and gift tags. This paper describes an interactive computational tool to assist in the design and construction of original iris folding patterns. The design of iris folding patterns is formulated as the calculation of a circumscribed polygonal sequence around a seed polygon. While it is possible to compute the positions of vertices analytically for a regular polygon, it is not straightforward to do so for irregular polygons. We give a numerical method for irregular polygons, which can be applied to arbitrary convex seed polygons. The user can quickly experiment with various patterns using the system prior to constructing the art-form.