Pneumocephalus is the presence of air or gas within the cranial cavity. It is usually associated with disruption of the skull: after head and facial trauma, tumors of the skull base, after neurosurgery or otorhinolaryngology, and rarely, spontaneously. Pneumocephalus can occur in scuba diving, but is very rare in this context. If there is a valve mechanism which allows air to enter the skull but prevents it from escaping, a tension pneumocephalus can occur (similar to what can happen in a tension pneumothorax). CT scans of patients with a tension pneumocephalus typically show air that compresses the frontal lobes of the brain, which results in a tented appearance of the brain in the skull known as the Mount Fuji sign. The name is derived from the resemblance of the brain to Mount Fuji in Japan, a volcano known for its symmetrical cone. In typical cases, there is a symmetrical depression near the midline (such as the crater of a volcano), due to intact bridging veins. Its occurrence seems to be limited to tension pneumocephalus (not occurring in pneumocephalus without tension). The sign was first described by a team of Japanese neurosurgeons.Pneumocephalus has also been shown to follow neurosurgical procedures such as deep brain stimulation and hematoma evacuation (e.g., chronic subdural hematoma), where while seemingly innocuous to the patient, may cause brain shift, subsequent stereotactic inaccuracy, and even another surgical intervention.
(These infinitely recursive corrugations are used only for embedding into three dimensions; they are not an intrinsic feature of the flat torus.) This is the first time that any such embedding was defined by explicit equations or depicted by computer graphics. Genus g surface
In the theory of surfaces there is another object, the "genus" g surface. Instead of the product of n circles, a genus g surface is the connected sum of g two-tori. To form a connected sum of two surfaces, remove from each the interior of a disk and "glue" the surfaces together along the boundary circles. To form the connected sum of more than two surfaces, sum two of them at a time until they are all connected. In this sense, a genus g surface resembles the surface of g doughnuts stuck together side by side, or a 2-sphere with g handles attached. As examples, a genus zero surface (without boundary) is the two-sphere while a genus one surface (without boundary) is the ordinary torus. The surfaces of higher genus are sometimes called n-holed tori (or, rarely, n-fold tori). The terms double torus and triple torus are also occasionally used. The classification theorem for surfaces states that every compact connected surface is topologically equivalent to either the sphere or the connect sum of some number of tori, disks, and real projective planes. Toroidal polyhedra
Polyhedra with the topological type of a torus are called toroidal polyhedra, and have Euler characteristic V − E + F = 0.