It has been shown before that dividing a pizza into 12 equal parts with at least one slice not touching the center is possible. For this, the researchers divided the pizza into six equal parts with three curved curves passing through the center instead of cutting the pizza with lines passing through the center and making an angle of 30 degrees with the last line. Then, by dividing these pieces into two, they obtained equal slices as in the figure.
University of Liverpool Dr. Joel Haddley and Ph.D. student Stephen Worsley developed the slicing method using these curves to produce slices with any odd number of edges. Then they divided these slices with an odd number of edges into two and obtained equal parts. For example, in the pizza images below, the pizza slices marked with different colors, cut only by curved curves passing through the center, have 5, 7, and 9 edges, respectively. By dividing each slice in half, equal parts are obtained.
Covering a plane with geometric shapes without spaces is called tessellation or tessellation in mathematics. The pavements formed by arranging the rectangular stones according to a certain rule exemplify tessellation. Covering a plane with a uniform geometric shape so that there are no gaps is called “monohedral tessellation.” Here the word mono means one, and the word hedral means shape. In this case, the patterns created with equal pizza slices are examples of monohedral tessellations.
You can find detailed information about the study here.