The simplest non-orientable surface on which the Petersen graph can be embedded without crossings is the projective plane. This is the embedding given by the hemi-dodecahedron construction of the Petersen graph (shown in the figure). The projective plane embedding can also be formed from the standard pentagonal drawing of the Petersen graph by placing a cross-cap within the five-point star at the center of the drawing, and routing the star edges through this cross-cap; the resulting drawing has six pentagonal faces. This construction forms a regular map and shows that the Petersen graph has non-orientable genus 1.