The FACE animation
FACE (Known as 赤の王様 "the Red King" in Japanese), is an event that occurs when Madotsuki opens the door at the top of the Stairway, in the Number World.
It shows a flashing animation that looks like some sort of face or mask. The animation fades in slowly from a black screen and is accompanied by a crescendoing rushing sound.
It cannot be skipped until it has been playing for approximately ten seconds. When the animation ends, Madotsuki awakens abruptly.
Interpretation
Some fans associate it (in conjunction with KyuuKyuu-Kun, who is found nearby) with evidence by some fans to support the theory that Madotsuki has some kind of trauma involving penises, either a rape, gender confusion or transexuality. The interpretation of FACE being a penis head further expresses this. Kyuukyuu-kun could be seen as evidence that Madotsuki was raped (some rapists get excited from seeing the victim struggle and not excited when the victim "happily" complies, hence why KyuuKyuu-kun rubs it faster with knife and slower with cat. Even though it could mean that KyuuKyuu-kun is Madotsuki's dream version of someone who could've raped her.), although this can be interpreted as any kind of penis fear.
Alternately, it has also been suggested that FACE could be a sleep paralysis hallucination, which fits with the inability to end the event by pressing any buttons, and the fact that Madotsuki awakes once the event ends.