Thanks for the link.
In the bible, the first 'ark' (a boat) is described as box-shaped - measuring 300X30X20 cubits. The second 'ark' is described as a much smaller box - measuring 2.5X1.5X1.5 cubits. This was used to carry around sacred relics (but also served as a very unreliable weapon). It would seem the basis of the Noah myth came from Mesopotamia, but the 'Babylon tablet' on display in the British Museum describes a completely different form of ark - made of wood and bitumen it was round with a diameter of 70 metres.

I gleaned this from Dilbeck's interesting dissertation. Commenting on the marking's displayed on Ghiberti's pyramid she writes -

"There are small Latin numbers marking the sides of Ghiberti‘s representation of the Ark. Across the right face of the Ark is -ccc? corresponding to three hundred. Across the breadth of the left face of the Ark on each plank: x, xx, xxx, xxxx, and xxxxx (fifty). The central plank also has numbers along is vertical face: x, xx, xxx (thirty). These measurements reflect the biblical story in which God commands -the length of the Ark three hundred cubits, its width fifty cubits, and its height thirty cubits...finish it to a cubit above? (Genesis 6:15).85 This attention to the detail of the Bible is significant and shows an obvious reliance on the biblical passage."
"Origen, an Egyptian Father of the Church envisioned the Ark as a truncated pyramid with three decks. St. Augustine agrees that the Ark had three decks. - Augustine also states that the Ark was built in the proportions of the human body, a notion that Ambrose develops at length [in De Noe et arca]...Alcuin accepts the older notion of the five deck Ark and so do many others, but all of the earlier writers thought of it as pyramidal in shape.? (Don Cameron Allen, The Legend of Noah: Renaissance Rationalism in Art, Science, and Letters [Urbana: Univ. of Illinois Press, 1963], 71)."

She also comments on the meaning of the iconography of the doors -

"The inclusion of the details referring to the prescribed measurements of the Ark may further emphasize it as a prefiguration of the Church. This may connect it to the Temple of Solomon, pictured in the last panel on the Gates of Paradise, which also has divinely prescribed measurements and is a prefiguration and model of the Church...Noah is a type of Christ and the Ark is an allegory of the Church...every panel contains a figure who prefigures or is a type of Christ."
"On the Gates Noah and his family come out of the Ark. They are reborn from the Ark with the sins of the world washed away and below their feet (in the guise of a dead human body now part of the earth). The family actually stands outside the door of the Ark and thus symbolizes the imagery of birth from the womb of the font, as in the above blessing, or from the womb of the Mother Church laboring to - bring forth new lives subject to the Christian law. The focus in the baptismal liturgy is on the rebirth, renewal, and regeneration possible through the blessed water of the font, and this is well illustrated on the Gates of Paradise by the post-Flood imagery."

"The obvious reliance on Origen for the representation of the Ark is another point Krautheimer used to support Traversari, a scholar of Origen. Clarke asserts that the pyramidal Ark need not rely on Origen, but that the biblical account would lead toward such a representation. In fact, Don Cameron Allen stated that all early writers thought of the Ark as a pyramid. As already pointed out, the small markings on Ghiberti‘s representation maps out the description found in the Bible. Even if the form of the Ark came from Origen, then Traversari need not have been the scholar to present it — Origen had already been translated into Latin and incorporated in the liturgy of Florentine lectionaries. Traversari was not the only scholar who showed interest in Origen or Greek writings."

From this it indeed seems that Ghiberti contrived a pyramid/ark to fit contemporary theological speculations - a synthetic device. The 3 'floors' running across the left side of the pyramid are at an angle, for a reason I suppose (he was an ardent champion of perspective). And why did he divide each face vertically into 5 'planks' if only to fit the biblical text? It all seems a bit arbitrary.

Origen lived in Egypt at a time when Egyptian culture was still a living entity and we don't know if Origen familiarized himself with it or to what extent. From his 'square' base to the enigmatic 'one cubit at the top' he comes up with a pyramid/ark which satisfies theological numerology. Yet he was surely aware of the actual monuments down the road from Alexandria - were these all arks too or did he just dismiss them as pagan? I must admit I don't know much about the particular situation in 2nd.C Egypt.