Preface - While this question may appear humorous, it is not "Purim Torah".
On Shmini Atzeret, there is a short "good-bye" to the Succah prayer which includes the wish that we should merit, next year, to sit in a succah composed of Leviathan skin.
I know very little about this Midrash, other than my understanding that the Leviathan is a gigantic sea monster and during the time of the Mashiach (?) all the righteous people will have a big feast in a succah composed of Leviathan skin.
I assume that if this were to be a "valid" succah, it needs schach, unless the term "succah" in this sense, is metaphoric. If it is a real succah, about how much shcach might be needed, and what would the schach be composed of? Is there any discussion about this?
(I was tempted to put a request for Leviathan skin on my neighborhood bulletin board, BTW :-)