Type 3: in this variety axial rotation is intermediate between the first two types with a rotation of being between 40 and 140.Another classification system divides total craniopagus twins into four categories:

Frontal: twins are facing each other with the axis of the bodies forming an acute angle
Temporoparietal: joined immediately above the external auditory meatus
Occipital: twins are connected in the occipital lobe causing the twins to face away from each other
Parietal: twins fuse at the vertex with the axis of the twins forming an obtuse angle; this leads to a situation where the twins share the most veins, lobes, and neural circuitry and thus is often described as one brain shared by two individuals
Having this kind of juncture means that there would be one common continuous cranium housing four cerebral hemispheres. An incomplete dural septum typically separates the flattened cerebral hemispheres. In total vertical craniopagus, the major cerebral arterial supply is usually confined to each respective twin and in some cases conjoined brain tissue may contain a larger artery. Within this category there are three smaller subdivisions that basically outline the different rotational symmetry of the junction. Partial
Stone and Goodrich define partial craniopagus twins as lacking substantial shared dural venous sinuses, with limited surface area involvement, with either intact crania or cranial defects. It is less common than total craniopagus twins. In partial craniopagus twins, the unions are usually frontal and less commonly occipital and vertical. Angular frontal junctions occur when the two twins are joined at any part of the forehead.
Craniopagus twins are conjoined twins that are fused at the cranium. The union may occur on any portion of the cranium, but does not primarily involve either the face or the foramen magnum; their brains are usually separate, but they may share some brain tissue. Conjoined twins are genetically identical and always share the same sex. The thorax and abdomen are separate and each twin has its own umbilicus and umbilical cord.The condition is extremely rare, with an incidence of approximately 1 in 2.5 million live births. An estimated 50 craniopagus twins born around the world every year as of 2021, with only 15 twins surviving beyond the first 30 days of life. Relatively few craniopagus twins survive the perinatal period; approximately 40% of conjoined twins are stillborn and an additional 33% die within the immediate perinatal period, usually from organ abnormalities and failure.However, 25% of craniopagus twins survive and may be considered for a surgical separation; several such attempts occur yearly worldwide. Advances in neuroimaging, neuroanesthesia, and neurosurgery have proven that a successful outcome is possible. Among all conjoined twins, craniopagus twins account for a mere 2% to 6%. Classification
The first classification system was developed by OConnell in 1976, where craniopagus twins were classified as total and partial. In the former, twins shared an "extensive surface area with widely connected cranial cavities", while in the latter, only a "limited, superficial surface area" was connected.In 2006, Stone and Goodrich came up with a more nuanced classification system, which is the "most commonly used" system.