Harry, Remus, Severus and Sirius flew up the mountain. When they arrived at its top, they realised that the thing was a cube shaped house - a cube with doors, windows and a flat top.

They landed. Sirius shouted "Alohomora!" and the door opened.

Harry was the second one to enter the cube. He found himself in an entrance hall, similar to the one at Hogwarts: a large, cavernous room, with a suit of armour on each side of the door. Curiously, the entire house seemed to consist only of an entrance hall... with a staircase to an upper floor that shouldn't be there.

"Weird," said Severus, echoing Harry's thoughts. "When viewed from outside, the house doesn't have two floors."

"Yes, it's weird. Maybe it just leads to a roof terrace," Remus suggested.

"There wasn't any roof terrace either," Severus replied.

Sirius was already climbing the staircase. Harry went after him, with Severus almost breathing down his neck.

"Lumos!" said Sirius.

Everyone gaped when they found themselves in another hall, with another staircase. There was an open door on each of the four walls of the hall. The door facing them led to the kitchen, where there was a wood stove; the left door led to a dining room, with a large wooden table and benches, and coats of arms and tapestries decorating its walls; the right door, to a study room, with two tables, four long benches, and shelves full of parchments; the door at their back led to a rustic lavatory.

"This is amazing!" Remus exclaimed. "Now I'm sure this house was made by Rowena. This is more than creative, this is..."

"Irritating," Severus snapped, but Harry knew he was enthralled.

"Let's split up," said Sirius. "Each one of us will take a different room and check everything carefully. We're looking for a wand, but we can't be sure of anything. Everything is suspicious until proven otherwise."

"You will take the lavatory," said Severus, clearly annoyed by being ordered around by Sirius.

Sirius shrugged. "Fine by me. There isn't much to be searched there. Go and search the study room, smart boy."

Severus arched an eyebrow and went into the study room. Harry knew that that was exactly where he wanted to go. Remus went into the kitchen, and Harry to the dining room.

Harry looked under the tables and benches, behind the tapestries and coats of arms. Nothing. He went back to the central hall, where Remus and Sirius were already waiting. Severus took a few minutes to return. No one had found any wand or anything else suspicious.

"Why don't we go upstairs?" Sirius suggested.

"Yeah," said Harry, placing his foot on the first step.

Sirius stopped him. "I'll go first."

Harry rolled his eyes, but let Sirius pass him by. He heard Sirius casting "Lumos" again.

They were in a bedroom with a solid canopy bed, with exquisite curtains and Ravenclaw's coat of arms on the wall above it. There were also two chests, a stool, a huge candelabra, tapestries on the walls, a rug on the floor, a fireplace and... another staircase leading to the upper floor. Severus opened one of the chests and started to search it. It contained dainty clothes in medieval style, very well preserved. Remus browsed through the other chest, which was full of papers, while Sirius checked the bed and Harry the tapestries. Severus was still putting everything back into the chest when Sirius began to climb the staircase.

On the third floor there was a workroom, with a spinning wheel, a few tables and shelves with all kinds of tools that they examined meticulously. Severus, more than anyone, wouldn't have felt satisfied if he hadn't turned everything upside down. There was also another staircase leading upstairs.

"I'm getting tired," Harry complained.

"Cheer up," said Sirius, climbing two steps at a time.

Harry followed after him and felt totally lost when he found himself in an entrance hall exactly like the one on the ground floor.

Harry looked at Severus and noticed he had paled. Remus was frowning. But Sirius was already opening the door through which they had entered the house. Or at least that was how it appeared.

Sirius went out, followed by Severus. Harry followed them, with Remus after him. Harry felt a wave of dizziness when, instead of seeing the mountain outside, he saw... the study room of the first floor. Harry was beginning to feel really confused.

"What the... What the heck is happening?"

The room had windows on all the walls, except on the wall where the door was. Remus walked to the wall opposite to the door, pulled the curtains open and looked through the window.

"Just as I supposed: this window opens into the entrance hall on the ground floor."

"But aren't we in the first floor study room?" asked Harry.

"Yes, we are."

"Then I don't understand."

"I have a theory, Harry," said Remus. "But I would like to check a thing or two before I explain it to you..."

Severus, who was examining the parchments again, shook his head. "Don't be long, Lupin. There is something rotten here."

Remus walked to the staircase. Harry sat at one of the study tables, and Sirius sat beside him.

Remus returned and announced, "The entrance hall is still downstairs."

"But it's also on this same floor," Harry protested.

"I know," said Remus.

Severus came nearer them. Harry could feel his frustration.

"Explain yourself, Lupin. Now."

"Sit down, all of you, please." Remus produced a few coins from his pocket. Severus sat in front of Harry; Remus sat beside Severus, facing Sirius. "These phenomena are happening because this house is a tesseract."

"A what?"

"A hypercube," said Severus, as much for himself as for Harry. "I see... Fascinating!" Severus stared intently at Harry, as he did when he wanted to explain to him something he considered important. "The tesseract is a square figure with a fourth dimension, like a cube has three and a square has two."

Harry tried to visualise it, but couldn't even get close to an idea of it.

Remus, however, had transfigured his coins into flexible cubes and was shaping a figurine with eight cubes forming an inverted double cross - four cubes piled up one on top of the other in a tower and another four cubes attached to each one of the exposed faces of the second cube from bottom-to-top.

"See? The bottom cube is the entrance hall. Then we climbed to the first floor, where the five cubes are forming a cross. Above the first floor, we have those two other floors, each one formed by a cube/room: the bedroom and the workroom."

"Right. But how do you explain that when we passed through the door of the ground floor we came back to the first floor?" asked Sirius.

"The problem is that this figurine I've built is a tesseract viewed in three dimensions, while in our real world it has four dimensions. In order to imagine it in four dimensions, you would have to tuck the top cube onto the bottom cube, and fold those side cubes in till they meet the top cube." Remus pointed his wand to the figure and made the cubes enter into each other as he had explained without really folding them.

Harry widened his eyes. "Blimey!"

"Rowena was a genius," said Sirius.

"This is all very enlightening and interesting, but the problem is we haven't found Rowena's wand anywhere," said Severus. "We have meticulously inspected every room."

"What if it's not even a wand we should be looking for?" Harry whinged.

"Why don't we go out, have lunch, take a rest and then think about the whole problem again?" Sirius suggested.

Remus scratched his head. "I'm not sure I know how to go out of this house."

"What?" exclaimed the other three.

Harry stood up, ran downstairs, opened the front door and found himself staring at his friends in the study room again.

Remus smiled. "I was going to warn you that it probably wouldn't work..."

"Hmph. I should've known. But I had to try."

"Very well, Lupin" hissed Severus. "What is your brilliant plan?"

Remus stood up and walked to the window on the left wall. "Ah-hah. Very interesting."

"What is it?" asked Sirius, joining him.

Harry and Severus approached them too. The window didn't open to the kitchen: it opened directly outside. Harry walked to the corner where the study room and the kitchen met in the central hall at ninety degrees.

"That's impossible," Harry protested. "That window is fifteen feet from the kitchen."

"Not in a tesseract," said Severus. "If you open that window and step through it, you will be in the kitchen.

Harry did exactly what Severus had suggested: he walked to the window, opened it and... "Aaaaaaaaaaaaaaaaaaaaaaah...."

It happened so fast that Harry didn't even have time to think. He fell, and fell, and fell. Luckily, he landed on high, soft grass. He was outside. He got up and flexed his sore muscles. He couldn't understand how that had happened, but it was great, because he had found an exit. He circled the house, entered through the front door, crossed the entrance hall, and climbed the staircase to the study room.

Sirius and Severus ran towards him and asked what had happened.

"I've found an exit," Harry announced triumphantly. "I fell out. I've been outside the house. You can do the same, but you'd better use your brooms."

"Have you hurt yourself, Harry?" asked Sirius.

Severus was touching Harry's sore shoulder with his wand. Harry noticed that Severus knew exactly where it hurt the most, and realised that Severus could feel Harry's pain when he was close enough.

"Don't worry, I'm okay. Let's go out and do what Sirius said: have lunch, take a rest and think things over before coming back here."

"Harry, I'm afraid it's not so easy," said Remus. "In a four-dimensional figure, a three-dimensional man has two choices every time he crosses an intersection line, like a wall or a threshold. Usually he will make a ninety-degree turn through the fourth dimension, but he doesn't feel it with his three dimensions. Stay close to the door and look."

Remus went out though the same window that Harry had fallen out of moments ago. As soon as he disappeared, they heard his voice coming from kitchen. "See?" Remus left the kitchen by the door and entered the central hall, and the four of them entered the study room again.

"So what you are saying is we can choose between falling out, like Harry did, or entering the kitchen?" asked Sirius.

"More or less. My theory is that Harry orientated himself subconsciously. He wanted, in his subconscious, to find the exit, and he found it."

Severus shook his head. "I wouldn't like to depend upon any subconscious orientation."

"I agree that it's scary, Severus," said Remus.

"Especially with a subconscious like yours," Sirius snapped.

"Yours must be even scarier," Severus snarled.

Harry thought that it would have been a hard match. Which one of the four would have scarier images in their subconscious? The mere thought made Harry shiver.

After a long silence, Sirius was the first to speak. "What if we go back to the workroom and check the windows?"

"Mathematically, it ought to look into the four side rooms in this floor," stated Remus. "But it won't do any harm to go and try."

They went upstairs and entered the workroom. The spinning wheel and the tool shelves were in the same place as before.

"From my understanding about the way a hypercube works, this room must be inside all the others," Severus commented.

"That's correct," said Remus. "We shall see... I believe this window must look into the kitchen."

Remus pulled the curtain from the north window. It didn't look into the kitchen. A wave of vertigo shook Harry. All of them tried to grip the curtains in order not to fall.

"Close that bloody thing, Lupin!" Severus shouted.

The window looked down instead of out, down from a terrifying height. Harry glimpsed the towers of a castle down there. "Hogwarts!"

"We're looking down from a point just above Hogwarts castle," said Sirius. "But don't ask me how that is possible."

"I think space is folded over through the fourth dimension here and we're looking past the fold," said Remus. "Why don't we try the other windows?"

Severus turned his back to the window and walked towards the east window. Harry followed him. When Severus opened the curtain, they saw a seascape; the vast ocean and the blue sky. However, the ocean was above the sky. Harry felt seasickness at the sight of the waves rolling overhead.

Sirius and Remus were at the opposite side of the room, at the west window.

"What can you see?" Harry asked them.

Sirius had paled. "Nothing."

"What do you mean, nothing?"

"Absolutely nothing. Nothing at all. It's terrible."

"I think we've just looked at a place where space is not," Remus mused.

"As for this window, it shows the ocean and the sky, but the ocean is above the sky," Harry summed up.

Severus was already walking to the south window, the only one they hadn't checked yet.

"Severus, wait," said Harry. "Remus said that our subconscious interferes with the way things work here. What if we all tried to concentrate and imagine the thing we most want to happen?"

"My subconscious is here and very well, thank you. I cannot get rid of it, and I don't believe any kind of concentration is necessary to activate it," Severus stated.

Harry wasn't in the mood to argue with Severus. Remus and Sirius closed their eyes to concentrate, and Harry did the same. He tried to visualise Rowena Ravenclaw's wand.

When he opened his eyes again, Severus had pulled the curtain just a bit and was peering through the window.

"What can you see, Severus?" asked Harry.

Severus turned around, with an enigmatic expression. "A rustic style cafe, with wooden tables and sunshades outside. There is no one outdoors, but I have just seen a white-haired wizard walking inside."

"Er, it seems our subconscious is hungry," said Harry. "What do you think?"

"Let's go out and have lunch, of course," said Sirius, changing the colour of his hair into hazel with red streaks and shortening it a bit, erasing any trace of beard, and changing the colour of his eyes into hazel too. "What do you think?"

Harry started. It wasn't that Sirius had become ugly; far from that. He just looked... softer. It wouldn't be easy to get used to his godfather's new look. Severus, in his turn, was inspecting Sirius from head to toe with a disgusted face.

Remus smiled. "I don't think I would be able to recognise you if I saw you on the street."

"Then it's perfect."

The "Rainbow Cafe" was a hexagonal wooden cabin. Harry was tired of cubes and other polyhedrons, but it was a pleasant place, surrounded by trees. Inside, the walls were creamy white; the tables, the chairs and the floor were in pale wood; the table-cloths and curtains were red and white chequered. Lily-shaped lamps hung from the ceiling.

The Cafe was empty, except for a blonde waitress who approached them and a barman who entered the kitchen as soon as they arrived. They decided to stay outdoors: they would be able to talk more freely and the scenery was lovely.

They sat on two long benches at a wooden table, under a giant sunshade: Harry and Severus on one side, Sirius and Remus on the other. Severus opened the menu and Harry read it over his shoulder.

Burgers, fish, scampi... Harry ordered the "All Day Breakfast": two rashers of lean back bacon, Scottish Lorne sausage, fried egg, hash browns. Sirius too. Severus ordered scampi with salad garnish; Remus, a veggie burger. They ordered Butterbeers for everyone. They were tired and hungry, and didn't talk much during lunch.

They weren't going to order desserts, but the waitress insisted so vehemently that they had to try the ice creams that they simply couldn't say no. Harry chose "The Loch Ness Monster": three scoops of mint chocolate chip ice cream, mint syrup, a Cadbury's chocolate flake plus whipped dairy cream and a scattering of dark chocolate chips; Sirius preferred "The Highland Midge Massacre": three scoops of double cream vanilla ice cream, raspberry sauce, crushed Oreo cookies plus whipped dairy cream and a cherry. Remus opted for the "Execution by Chocolate": mammoth chocolate chip muffin sliced and buried under three scoops of double chocolate chip ice cream topped with chocolate and raspberry sauce and dark chocolate chips plus whipped dairy cream and a cherry. Severus ordered the "Execution by Chocolate" too, but with no cream or cherry.

This time, however, instead of the waitress who was serving them, a white-haired old wizard brought their ice creams. When he came close, Harry almost choked on his Butterbeer. It was Florean Fortescue.

Under the suspicious looks of the four wizards, Fortescue winked at Harry, distributed the ice creams, conjured a chair and sat down at the head of the table. "You are right on time."

Remus greeted him with a nod. "We are glad to find you in good health, Mr Fortescue. Were you waiting for us?"

"Oh, in a way, yes. It's a long story, which I shall try to sum up. I shall probably have finished it when you finish your ice creams."

"What's the hurry?" asked Severus sardonically.

"Mr Snape, every second is precious in our modern world. The ice creams are melting; help yourselves, please."

Suddenly, "The Loch Ness Monster" didn't look as delicious as before. Harry was anxiously waiting to hear Mr Fortescue's story.

"You have arrived here, so you must have followed in our footsteps, so to speak. Hence you must know we found Rowena's esplumeor in 1947. We were young and enthusiasts of the medieval past. We believed Riddle shared our ideals. Together, we searched for Rowena's wand, and failed to find it. We agreed to come back another day and continue with the search. But Riddle betrayed us: he came here alone, found Rowena's wand and transformed it into a Horcrux."

"If he came alone, how did you find out what he did?" asked Sirius.

"Mr Black..."

Sirius widened his eyes. "How have you... What gave me away?"

"Oh, your father was a great friend of mine. He was a member of our group, as you must know... Your posture and gestures remind me of him. Don't worry; I will not disclose your secret, if you don't disclose mine."

"This is hogwash," Severus snapped. "Ollivander is a Legilimens. He used Polyjuice Potion to disguise himself as a waitress. I saw the waitress talking to Fortescue inside the Cafe a few minutes ago, while we were eating. It was Ollivander who told Fortescue about Black's identity."

Sirius, Harry and Remus broke out with all kinds of expletives, between surprise and anger, while Fortescue burst into laughter.

"Brilliant! And how did you arrive at this conclusion, Mr Snape?"

"I smelled Polyjuice Potion when the waitress approached us. Then I noticed how fixedly she looked into our eyes. I had to use Occlumency to block her."

"Very clever, very clever." The waitress showed up at the door, and Fortescue winked at her. "But please, eat your ice creams and let me finish the story."

Harry looked at his ice cream suspiciously. There was something tricky going on. What if the ice cream had been poisoned? But Severus looked intently at him and tranquilised him by devouring a spoon full of "Execution by Chocolate".

Fortescue cleared his throat. "You are on the right track. Riddle was neither a Legilimens nor an Occlumens back then. Ollivander is older than he, and was already an accomplished Legilimens. It wasn't difficult for Ollivander to find out what Riddle had done. Riddle had found Rowena's wand in the central point of the esplumeor, the geometrical centre of the tesseract. The wand was invisible, but if you concentrated your mind and passed exactly by that point, you could fetch it. Riddle managed to do it. Then he cast the Horcrux spell over the wand. Arrogant as he is, he believed no one else would be able to find it, and left it in the same place." Fortescue ran his eyes over anyone at the table, and breathed deeply. "Ollivander told us what he had seen in Riddle's mind and we three came back here to fetch the wand."

"We three?" asked Sirius.

"Ollivander, your father, and I."

"My father? My father came here with you? Was my father one of those who found the esplumeor? To whom were you referring to when you said 'we'?"

"Ollivander, your father and I, as I have just told you." A perplexed silence fell upon them before Fortescue, evidently anxious to finish his story, continued. "Your father was a very stubborn and arrogant man, Mr Black. He insisted he was the most apt to hide Ravenclaw's wand. Ollivander and I have always been peaceful men, so we let him take the wand. Furthermore, none of us knew what exactly a Horcrux was, let alone how to destroy it. In a certain way, your father lifted a heavy weight from our shoulders."

Sirius groaned. "Don't tell me the wand has been in 12 Grimmauld Place all this time!"

At that moment, the waitress transformed into Ollivander again - white hair, silvery eyes shining like moons - and conjured another chair at the other head of the table. He greeted everyone with a polite nod, but with a distant light in his eerie moon-like eyes, and sat down.

"Calm down, Mr Black," said Ollivander. "This specific point will soon be clarified."

"Voldemort came back and found out that you had taken the wand," Harry tried to guess.

"Florean and I talked a lot about that... It's not You-Know-Who's style to go back and check anything... So, we believe his intention was to use Rowena's wand, since he cannot defeat Harry Potter with his own wand." Ollivander stared at Harry for a long time. "We suppose - and this is only a supposition - he must have come here and found out that the wand was not where he had left it. Then he sent his minions after us. As they are not very clever, they didn't attack us simultaneously. They ransacked Fortescue's Ice Cream Parlour first. As soon as I saw the destruction they had caused in Fortescue's place, I knew who they were and what they were looking for. I disappeared from sight as fast as I could. I didn't feel inclined to meet those beasts and especially You-Know-Who again."

"And yet the wand wasn't with either of you two," said Remus, his eyes twinkling.

"That's absolutely correct, Mr Lupin. Yew wood, twelve inches, dragon heartstring..." Ollivander reached out and caught the wand Sirius had placed on the table. "It's a beautiful and powerful wand, Mr Black."

The astonishment was general, or almost. "What?! B-but..." Harry stammered.

"When I left Azkaban," Sirius explained, "I didn't have a wand. I've found this one in 12 Grimmauld Place. I knew it wasn't my parents' or Regulus's - I wouldn't use a wand that had belonged to any member of my family. I didn't know whose wand it was. It suited me well, so I decided to keep it."

"Congratulations, Mr Black. This is Rowena Ravenclaw's wand."

When they could breathe again, Severus stood up, clearly nervous. "Everything seems perfect, but I am not convinced. There is something wrong."

"Why do you think so?" asked Harry.

"Doesn't it strike you as a remarkable coincidence the fact that they..." Severus nodded at Ollivander and Fortescue "are here, precisely here? How did Fortescue survive the Death Eater's attack? Why have the two of them come to the most obvious place, the place where everybody would look for them?"

Fortescue stood up at the head of the table. Ollivander stood up too, and came close to him.

"Gentlemen, Ollivander and I are just a projection of your collective subconscious. Everything you see... the Cafe, the ice creams... has been created conjointly by yourselves. Everything we have told you were facts that were already in your subconscious."

"Remus's theory of the subconscious orientation!" Sirius exclaimed.

"That's amazing. I know my theory predicted this possibility, but..."

"Do you remember when I asked you to concentrate before Severus pulled open the last window curtain?" asked Harry.

"What you are saying is that... No. I cannot believe my subconscious has contributed to this!" protested Severus, pointing at the table full of empty ice cream bowls.

Sirius smirked. "Including your blonde Polyjuiced waitress. Admit it, Snape: we are a hell of a quartet." Sirius handed his wand to Severus. "Would you be so kind as to extract the Horcrux from it, since it's my wand?"

"Why me? Why don't you ask your beloved werewolf?"

"I don't want to risk his life."

Severus narrowed his eyes at Sirius. "How do I know that your bloody wand will not curse me as the ring cursed Albus?"

"I've been using this wand for almost a year now. If it were cursed, I don't think I would be here to tell the story. Albus told me it wasn't the Horcrux spell that cursed him; it was a curse put specifically on the ring. Did Albus teach you how to extract a Horcrux from an object?"

"Of course he did." Severus sighed and caught Sirius's wand. Then he put it on one of the benches and pointed his wand at it. "Expellianimula!"

A green light left the wand and spread around the whole area. When the glow subsided, Sirius took his wand. "Mr Ollivander, Mr Fortescue, it was a pleasure to meet you. Farewell. Harry, come here. Friends, let's go back home."

Notes:
1. The tesseract plot was borrowed from the classic Sci-Fi short story "And he built a crooked house", by Robert A. Heinlein, which you can read here.
2. The "Rainbow Cafe" (and its menu!) is based on a real place near Loch Ness. I won't mention its real name because I don't think its owners would like to have their name associated to a slash story ;-).