Last time MAT 103 creator Margaret Groman taught the course (Spring 1999) she was given a remarkable souvenir by her graduating student Crystal Henry:

Here is the story, in Crystal's own words:

The first pattern comes from the Iroquois border designs. It is an one-dimensional pattern known as a p111, translation only.

The next pattern is an Ojibwa design used on beaded belts. It has translation and horizontal reflection, which makes it a p1m1.

The next four designs are all Iroquois designs used for quiltwork, bead work and applique on garments and maccasins.

The first one is a pm11 because it has translation and vertical reflection.

The second is a p112, which has translation and rotation.

The third border design has glide reflection with translation which makes it a p1a1.

The fourth is a pmm2, because it has translation, horizontal and vertical reflection with rotation.

The last pattern is an Ojibwa design used on beaded belts. It is known as a pma2 which has all the isometries except horizontal reflection.

I used Iroquois and Ojibwa designs because they are part of my heritage. I am half Ojibwa and half Oneida, one of the Iroquois tribes. I've researched the designs at the library, then drew each out individually on tracing paper. After that I transferred the images to a silk screen and printed out on paper. I' ve found the seven possible combinations of isometries from my own culture, using one-dimensional patterns.


Lyford, Carrie A. Iroquois Crafts. Wisconsin: R. Schneider, 1982.

Lyford, Carrie A. Ojibwa Crafts. Kansas: Haskell Institute, 1943.

Naylor, Maria, ed. Authentic Indian Designs. New York: Dover Publications, 1975.

Farmer, David W. Groups and Symmetry. American Mathematical Society, 1996.