by Doris Schattschneider, Moravian College, Bethlehem,
Pennsylvania (from the Discovering Geometry NEWSLETTER, vol. 7,
no.,1, Spring 1996) It is easy to show that every triangle
tessellates and every quadrilateral tessellates. One way is to
simply rotate the polygon by 180 degrees about the midpoints of
each of the figure's sides and repeat this procedure again But
the regular pentagon does not tessellate, so not every pentagon
Is there at least one pentagon that will tessellate? Yes, there
are many. But how many? Prior to 1968, it was thought that all
tessellating pentagons could be classified into five types. But
in that year R. Kershner found three more types and thought that
the problem had been solved. No further discoveries were made
until 1975, when Martin Gardner wrote a column in Scientific
American based on Kershner’s article. Soon Gardner reported the
discovery of another type found by one of his readers, Richard
James III. James had cleverly taken the familiar tiling by
octagons and squares, separ