This quilt was designed and crafted by Lisbeth G Clemens in the summer, 1993. It is based on one of the aperiodic tilings using "kites" and "darts" due to Roger Penrose. The following link shows an enlarged view of the quilt. The grid or tiling used in designing the quilt is shown above. This figure is from Tilings and Patterns, Branko Grunbaum and G.C. Shephard (WH Freeman and Co, 1987), page 544. Those interested in the maths can look in this book for further information. The tiles used in the quilt are referred to as the "P2 set" in Grunbaum and Shephard.
(Other quilts by Lis - a "gallery" with many of her quilts.)
The following (not-to-scale) diagram gives the details necessary to construct the kite and dart shapes (the P2 tiles) used in the quilt, if you want to construct them yourself.