"buckypumpkin" represents a C60 buckminsterfullerene molecule. The molecule, popularly called a "buckyball," takes the form of a truncated icosahedron. The discoverers of the C60 form of carbon named the molecule after architech Buckminster Fuller, who made use of geodesic dome shapes in his work. The 1996 Nobel Prize in Chemistry was awarded to the scientists who discovered the process for synthesizing this form of carbon, and variations on it (such as "buckytubes").
On the pumpkin, the locations of the carbon atoms are represented by holes drilled completely through the pumpkin flesh at the verteces of the truncated icosahedron, and the carbon-carbon bonds are represented by lines cut only part of the way through the flesh, with double bonds indicated by double lines. Ordinarily, a truncated icosahedron would be most familiar as the shape of a traditional soccer ball (sewn together from black pentagonal patches and white hexagonal patches). The pattern goes all the way around the pumpkin.