The story is "Sleeping Beauty."
The main character, Nakajima Kasumi, tells us that Fujino Yuki, who's been a good friend of hers since elementary school, is really beautiful when she sleeps. She's cute when she's awake, too, but when she sleeps, she's the cutest thing ever. It often happens that she falls asleep while the two of them are studying in the library and the boys sitting across from them can't take their eyes off her. And sometimes they'll be in the park, sitting on a bench, and she'll sleep on Kasumi's shoulder. When that happens, Kasumi checks to be sure she's asleep and to be sure nobody's around, then does things like putting her cheek against Yuki's, sniffing Yuki's hair, etc. And she whispers in her ear that she loves her, something she'd never dare to do while Yuki was awake. Not only does she love Yuki's sleeping face, she loves Yuki herself.
Yuki wakes up, apologizes for sleeping so long, and tells Kasumi she should have woken her up, as she let her sleep for two hours. Kasumi tells her it's all right since she likes looking at Yuki's sleeping face, and Yuki tells Kasumi she's weird. lol
Then one day, Yuki tells Kasumi that she's moving to Osaka. Then Kasumi tells her she loves her, and has since elementary school. Yuki tells Kasumi she loves(/likes?) her too, and so Kasumi explains that her love for Yuki is in the sense of what one feels for a lover. After that, Yuki didn't appear at school again.
It's Valentine's Day. Kasumi runs into the girl who I believe is the female protagonist of Discommunication, Togawa, in the bathroom and lends her her handkerchief. She asks Togawa if she knows Yuki's whereabouts--she's been out of school for three days, and Kasumi asked Yuki's family where she was and they told her Yuki was staying with a friend and hadn't come home yet. Togawa is in Yuki's class, so Kasumi thinks she might know something.
Togawa tells Kasumi that she doesn't know anything, and goes on to say that if anyone knows stuff about Yuki it should be Kasumi herself, since the two of them are always together. In fact, in middle school Togawa and her friends joked that the two of them were a couple.
Kasumi tells Togawa that she confessed her feelings to Yuki three days ago, and that she's worried that's the cause of Yuki's absence from school. Togawa is surprised, but then says "So you really do like her?" Kasumi tells her that of course she just likes Yuki as a friend. Just then, some other girls come into the bathroom, and Kasumi hightails it out of there.
Buying chocolates for her boyfriend (I think), Togawa looks at them and wonders why food you have to give away always looks so darn good. lol.
Just then, she sees Yuki with Matsubue, who I think is the male protagonist of Discommunication, in the park.
Matsubue wakes Yuki up. She thanks him for waking her up. When Togawa asks what's going on, Matsubue tells her that he found Yuki collapsed outside his house when he went out to get the paper that morning. He turned the paper into a harisen (paper fan) and smacked Yuki with it to wake her up. He was pleasantly surprised that she was alive... lol.
She asked him to stay with her during the day and wake her up if she started drifting off. She has to make it until seven without sleeping, for some reason.
It turns out that Yuki hasn't slept at all for the past three days. She couldn't stay at home because she'd get sleepy if she was there, so she's been walking around. When Togawa asks why she has to stay awake, Yuki tells her that someone confessed their feelings to her three days ago, and so certain circumstances have arisen that require her to stay awake for three days. Togawa immediately connects this with Kasumi, though she doesn't say so aloud.
Yuki suddenly realizes she needs to bathe, as she hasn't at all during the last three days. She asks Matsubue if she can use the bath at his house, and he says yes.
As Yuki is getting in the bath, Togawa asks her why she suddenly feels the need to bathe, and Yuki replies that tonight she's going to sleep with that person who confessed to her. Togawa immediately assumes something perverted, and blushes. lol
Yuki asks Togawa to call Kasumi and ask her to come over there at seven. When Kasumi gets there, Yuki apologizes to her for not noticing Kasumi's feelings for her during all their years together. When Kasumi confessed to her, she began to consider whether she could respond to Kasumi's feelings. Unfortunately, she realized that she couldn't see Kasumi as a lover. But she thinks that Kasumi is the best friend ever, so as an apology, she wants to give Kasumi the thing Kasumi likes most--her (Yuki's) sleeping face.
Yuki decided to stay awake from the time Kasumi confessed until exactly three days from then, which would work out to be Valentine's Day. Her reasoning in doing this was that since she's never stayed awake for three days on end, her sleeping face now will be the best one she's ever had. lol.
She then goes on to tell Kasumi that if she still wants to kiss, embrace, and touch her (words Kasumi used during her love confession), she can do it while Yuki is asleep, because she'll be sleeping so deeply she won't remember a thing. That's why she took that bath earlier.
It's her Valentine's Day present to Kasumi.
As Yuki is drifting off, she tells Kasumi she's glad she met her.
Togawa and Matsubue comment that she's really fast asleep right now, so much so that even hitting her with the harisen wouldn't wake her up. lol. They go on to say that she looks happy.
Togawa asks Kasumi if she's really going to fool around with Yuki, and Matsubue offers to buy them some cup noodles and let them use a room in his house in place of a hotel.
Kasumi is confused and doesn't understand her own feelings anymore.
Matsubue notices that the moon looks nice that night, and brings a futon outside for Yuki and Kasumi of them to sleep in. Kasumi falls asleep.
Then Togawa suggests that she and Matsubue sleep outside as well, so the four of them end up sleeping outside under the moon. Matsubue uses some sort of moon magic or something on Yuki and Kasumi, and then they wake up.
Yuki tells Kasumi she just had a dream about the two of them playing together right after they met, in their first year of elementary school. Kasumi says she had the same dream.
Kasumi tells Yuki that she was afraid Yuki wouldn't want to see her ever again after her confession. She asks Yuki if she'll write her while she's away in Osaka, and if she can go to visit Yuki during breaks. In short, if they can remain friends.
Yuki answers, "Of course!"
In the very last panel, Matsubue asks Togawa where his Valentine's chocolates are, since he expected her to give him some, and she tells him they looked so good that she ate them on her way over. lol Matsubue silently gets angry.