But there is a limit on how much work they can do on the issue for now, as the magazines are produced, designed and published, within 24 hours.
Strictly speaking, the team have previously carried out the odd bit of preparatory work in advance, but according to the editor's note in the latest issue, "the bulk of the work: the commissions, the transcriptions, the interviews, the research, the writing, the editing, the design: we did it all in one day".
The magazine, which is built around a different theme each time, is now produced by the group of Edinburgh University students from the bedroom of current editor Lydia Willgress, a third-year English literature student.
Speaking to Journalism.co.uk, she said the idea was inspired by a company which runs 24-hour magazines in the US.
Willgress is also deputy editor of the university's history, classics and archaeology journal Retrospect. The project involves members of the same team but is a separate title.
The first 24-hour edition was produced in November, with Retrospect editor Will Ellis as editor of the 24-hour magazine. The second followed around a month later, and the third was published in January. The next one is due for April, giving the team time to focus on their university studies.
"The reason we decided to create one in 24 hours was the pressure to see what you could create in 24 hours in comparison to a weekly or monthly," Wilgress told Journalism.co.uk.
"But also because if you create a whole magazine in 24 hours and you do it again and again, it's always going to be different if you have different teams and different writers and you have a different theme, different people involved.
"Because there's such a time constraint on it, I don't think you have time to think about the similarities between say this magazine and the last one. So I think it's a bit more dynamic and also I think it's quite an interesting concept for people to look at for the online industry in particular."
When it comes to producing a 24-hour magazine, she said "everyone does them differently".
"All the ones I've seen so far have all been different. Some people do them mainly features-based, or they pick a theme out the hat in the morning because the idea is to write, edit, design and create the whole magazine in 24 hours.
"So, technically, the people that bought the idea about, say that you're not meant to do any preparation for the magazine before that 24 hours.
"But we changed this slightly, because we're student journalists and should just get our names a bit more out there."
The first edition - which was completed in 23 and a half hours - included features written by professional journalists she said, although the writers in the last two editions have all been students.
The first edition saw a readership of around 8,000 people within the first 2 days following publication, she said.
"We're not earning money from it but we wanted a good enough readership to be able to motivate ourselves to stay out for another 24 hours," she said.
The latest edition, which she said was blogged about by Richard Branson - the magazine featured an interview with his son - recorded a readership of more than 20,000 within two days, she said.
"I don't know if the next one will be ever as good as that one but we shall try!"
In the future the team may look at ways to "try and incorporate advertising", she said, but added that they are "not sure on that".
"We quite like the fact that we're just content-based and obviously if we incorporated advertising then we would make it longer so we still had the same amount of content, so it wasn't like we were filling up pages just by placing an advert in there."