The horn of a rhinoceros is made of many fused hair-like growths. Therefore, as one would expect, there is only a dense structure of highly keratinized tissue throughout the horn to its base. At the base of the horn there are special follicle-like tissues which add keratin to the length of the horn.
The horns of cattle, sheep, and antelope are considered to be true horn. The outside of the horn is derived from a highly keratinized epidermis. Dermal tissue is found deep to the keratinized covering. Bone develops in the central core of the horn.
Antlers are grown and shed annually by males of many species in the deer family. The antler has an epidermis with hair (velvet), and a dermis to support the epidermal covering while the antler grows. The epidermis and dermis cover a growing bone that forms the shape of the antler. After the antler reaches its mature size the epidermis and dermis are shed and the bone is all that remains.
The giraffe horn is much like an antler in its anatomy. There is an epidermis with hair and a dermis and bone beneath, but these layers are never shed and the structure is not lost annually, but persists for the life of the giraffe.