AbstractIt is well known that there are 17 crystallographic groups that determine the possible tessellations of the Euclidean plane. We approach them from an unusual point of view. Corresponding to each crystallographic group there is an orbifold. We show how to think of the orbifolds as artifacts that serve to create tessellations. Additional informationNotes on contributorsH. M. HildenHUGH M. (MIKE) HILDEN was born in New York, but has spent the past thirty five years in Hawaii. He received his doctorate from Stevens Institute of Technology, Hoboken, New Jersey in 1968. He has been a member of the University of Hawaii mathematics department since 1970. His main mathematical interests are low-dimensional geometry and topology, manifolds, and knot theory. His hobbies have included languages, handball, windsurfing, chess, pool, and drawing. He likes to travel and has spent a lot of time in Europe and South America.J. M. MontesinosJOSÉ MARÍA MONTESINOS-AMILIBIA was born and raised in San Sebastian, Spain. He received a doctorate from Universidad Complutense, Madrid in 1971. He was a member of the Institute for Advanced Study in Princeton from 1976 to 1978, and he also was a member of MSRI-Berkeley in 1985. He has been a member of the Spanish Royal Academy since 1990. His main mathematical interest is low-dimensional topology, in particular knot theory. His hobbies are mineralogy and crystallography. He has a large collection of beautiful samples of minerals.D. M. TejadaDÉBORA MARÍA TEJADA-JIMÉNEZ was born in Colombia. She obtained her doctorate in algebra in 1981, from the University of Montpellier, France. She obtained her Ph.D. in topology in 1993 from the University of North Texas. Since 1981 she has been a professor of mathematics at the Universidad Nacional de Colombia, Medellín. Her area of interest is knot theory. She is also interested in the mathematical foundations of architectural form and urbanism.M. M. ToroMARGARITA MARÍA TORO-VILLEGAS was born in Medellín, Colombia. She received her B.A. from Universidad Nacional de Colombia, Medellín, and her Ph.D. from the University of Cincinnati. She currently teaches at Universidad Nacional de Colombia, Medellín. Her mathematical areas of interest are algebra and knot theory. She likes to crochet and is an avid gardener