The Gemmorah learns the obligation of Succah from the Clouds of Glory that surrounded the Jewish people on Exodus (and later).
It also learns (at least one opinion) that the Schach must resemble a Cloud that "stems from the soil and is not impure" (Succah 11b).
IIRC there were a total of 7 clouds - one in every direction and one in front of the camp.
Bearing that resemblance, I'd expect the whole Succah to be made of Schach including the floor, likening the Clouds of Glory. Considering the minimal size of 80x80x80cm that would not be so difficult. As we all know that's not a requirement.