We study and catalog isoperimetric, planar tilings by unit-area Cairo and Prismatic pentagons. In particular, in counterpoint to the five wallpaper symmetry groups known to occur in Cairo-Prismatic tilings, we show that the five with order three rotational symmetry cannot occur.

Author Bio

John Berry will graduate from Williams College in 2016 with a major in mathematics. He plans to return to Williams the following year as an assistant wrestling coach before attending mathematics graduate school.

Matthew Dannenberg will be graduating Harvey Mudd College in 2016 with a double major in mathematics and physics. In the fall of 2016 he will enter the Ph.D. program at Stony Brook University to pursue his interests in geometric analysis and mathematical physics.

Jason Liang is an undergraduate math major graduating in 2016. His hobbies include animals and skating.

Yingyi Zeng is from Shanghai, China. She is a student from St. Mary’s College with a double major in mathematics and economics and a minor in computer science. After graduation, she plans to teach in the countryside of China for one year before attending graduate school in the U.S.