The Four Horn Jacob is a small, multi-horned, piebald sheep that resembles a goat in its conformation. However, it is not the only breed that can produce polycerate or piebald offspring. Other polycerate breeds include the Hebridean, Icelandic, Manx Loaghtan, and the Navajo-Churro, and other piebald breeds include the Finnsheep and the West African Dwarf.
Mature rams (males) weigh about 54 to 82 kg (120 to 180 lb), while ewes (females) weigh about 36 to 54 kg (80 to 120 lb). The body frame is long, with a straight back and a rump that slopes toward the base of the tail. The rams have short scrotums free of wool which hold the testicles closer to the body than those of modern breeds, while the ewes have small udders free of wool that are also held closer to the body than those of modern breeds. The head is slender and triangular, and clear of wool forward of the horns and on the cheeks. The tail is long and woolly, extending almost to the hock if it has not been docked. Jacob owners do not usually dock the tail completely, even for market sheep, but instead leave several inches (several centimetres) to cover the anus and vulva. The legs are medium-length, slender, free of wool below the knees, and preferably white with or without coloured patches. The hooves are black or striped. It is not unusual for Jacobs to be cow-hocked. They provide a lean carcass with little external fat, with a high yield of meat compared to more improved breeds.
The most distinguishing features of the Jacob are their four horns, although they may have as few as two or as many as six. Both sexes are always horned, and the rams tend to have larger and more impressive horns.Two-horned rams typically have horizontal double-curled horns. Four-horned rams have two vertical centre horns which may be 61 cm (2 ft) or more in length, and two smaller side horns, which grow down along the sides of the head. The horns on the ewe are smaller in diameter, shorter in length and appear more delicate than those of the ram. British Jacobs most often have two horns, while American Jacobs are more often polycerate. Polled (hornless) sheep are not registrable, since this trait is considered an indication of past cross-breeding, and as such there is no such thing as a polled purebred Jacob.
The horns are normally black, but may be black and white striped; white horns are undesirable. Ideally, horns are smooth and balanced, strongly attached to the skull, and grow in a way that does not impede the animal's sight or grazing abilities. Rams have larger horns than ewes. The horns in two-horned sheep, and the lower horns in four-horned animals, grow in a spiral shape. The rostral set of horns usually extend upwards and outwards, while the caudal set of horns curls downwards along the side of the head and neck. On polycerate animals it is preferred that there is a fleshy gap between the two pairs of horns. Partial or deformed horns that are not firmly attached to the skull, often referred to as "scurs", are not unusual but are considered undesirable.
information courtesy of https://en.wikipedia.org/wiki/Jacob_sheep