Followers of the Survival Strategy have proven themselves to be loyal to the Penguin Queen by replicating the Mysterious Penguin Hat in origami form, from stalking anime Mawaru Penguindrum.
The following are the printouts to fold your own Penguin Hat;
The hat has seems that go through the origami, so here's a better images to show the lines;
And as for the steps, 2ch has provided a series to haphazardly placed images that seems like the steps to make the hat;
Papercraft has suddenly gotten popular in Japan, probably thanks to Cospa and their line of GRAPHIG papercraft.
I might try this out myself when I've got time. Let me know if you've managed to make it yourself ^^
And normal A4 is fine, according to the original poster.
Tomorrow will post about how to make your very own Penguins #1, #2 and #3! ( ´∀`)