This section is from the book "Anatomy Of The Arteries Of The Human Body", by John Hatch Power. Also available from Amazon: Anatomy of the Arteries of the Human Body, with the Descriptive Anatomy of the Heart.
Some years back I observed a very remarkable variety in a subject at the Carmichael, then the Richmond Hospital School of Medicine: in this subject there was no common carotid on the right side; and the external and internal carotids arose separately from the arch of the aorta. The order of the vessels was,—right subclavian, right external carotid, right internal carotid, left common carotid, left subclavian. I showed this preparation to the younger Tiedemann when he visited the school, and he remarked, that no similar case had been observed or heard of by himself or his father. Mr. Harrison states that he has known two examples of the internal and external carotids arising on one side separately from the aorta.
* Velpeau's Surg. Anat., American Trans., p. 433.
In some cases the common carotid is crossed in front by the inferior thyroid artery. In other cases the vertebral artery ascends behind it to pierce the third or second cervical vertebra. Cases are recorded in which the common carotid ascended behind the angle of the lower jaw before it bifurcated; and on the other hand, it may bifurcate as low as the inferior margin of the thyroid cartilage, or at the sixth cervical vertebra: lastly, it sometimes happens, that there is no bifurcation,—the common carotid and internal carotid forming a continuous trunk, which gives off the branches of the external carotid. The common carotid may give off the inferior thyroid, superior laryngeal, pharyngea ascendens, superior thyroid and right vertebral arteries.
This artery sometimes arises by a trunk common to it and the lingual, or it may arise directly from the common carotid: in some cases the common carotid, instead of bifurcating, divides into three branches, the internal carotid, the external carotid, and the superior thyroid.