We consider the morphology of new fullerene families having negative Gaussian curvature formed by the introduction of 7- or 8-membered rings in a graphite sheet. The objects of our interest include the hypothetical structures of fullerene donuts and graphitic sponges. Their geometries are discussed based on the projection method on a honeycomb sheet which we have developed for normal fullerenes. Special emphasis is put on the new construction method for the structures of graphitic sponges. We demonstrate new carbon forms with three dimensionally periodic network based on polyhedral packing in space. The method can be applied to examine the local structures of amorphous carbon systems.