One of the common questions that people have about the facsimiles in the Book of Abraham is "How do Joseph Smith's interpretations match with those of the ancient Egyptians?" As a preliminary step to answering this very question, Michael Lyon has been gathering examples of hypocephali for years and has shared his information with John Gee and others. Gee analyzed the data to try to determine what the Egyptian identification of the figures was. In 2001, he published an article in Le lotus qui sort de terre, a collection of Egyptological essays in honor of Edith Varga, one of the leading experts on hypocephali.
The article, "Towards an Interpretation of Hypocephali," includes a preliminary typology of hypocephali (Facsimile 2 is a type III hypocephalus), a concordance of various numbering systems for hypocephali, a methodology for studying hypocephali, and, as a preliminary step in that direction, a list of ancient Egyptian identifications for various figures found in hypocephali. The list, gathered from multiple hypocephali, shows that most modern Egyptological identifications of figures in hypocephali do not match those of the ancient Egyptians. This means that while the Egyptologists' interpretations of the facsimiles do not match Joseph Smith's, they do not match the ancient Egyptians' either. As Gee writes, "If we ignore the ancient Egyptian identifications of the various figures in the hypocephali, we will construct an understanding of hypocephali that bears no resemblance to the ancient Egyptian understanding. We will, in short, not understand [hypocephali] at all."
At recent academic conferences, Gee showed that some of the Egyptian phrases associated with hypocephali have been mistranslated. His expanded typology includes three new types of hypocephali, none of which are round.
An answer to the question "How do Joseph Smith's interpretations match with those of the ancient Egyptians?" is currently premature and may never be conclusive, but we may finally be taking steps in the right direction.