At first glance, poetry and the finite geometry of projective planes seem far apart. However, there is a history of overlap between combinatorial mathematics and poetry, stretching back at least to the twelfth-century sestinas of poet Arnaut Daniel. This intersection remained vibrant during the twentieth century through the works of OULIPO, and we will describe our own recent exploration of the o Rubáiyát of Omar Khayyám using graph theory. After a short introduction to finite projective planes, including a brief discussion of questions of existence, we will introduce the process of composing poetry using a finite projective plane as a guide. We discuss a classroom activity we implemented in a creative writing class in which students composed poetry based on the Fano plane, and we present a plan for expanding upon this activity. Included here are several examples of such poems, including students' work, and some suggestions for anyone interested in writing poetry in this style.