sacred geometry, part 1: tesseract

“For a building built by an eccentric architect who supposedly belonged to a modern Pythagorean mystery cult, this hotel looks disappointingly normal,” thought Scarlett. She yawned, set down her bag, and pressed the elevator button.

The drive down from Cleveland had taken three hours, thanks to a wreck on the highway, and she was already tired from staying up the night before doing research. She’d heard about Hotel Tetra from one of the readers of her blog, Things That Go Bump in the Night. The reader claimed that the architect of the hotel, Paul van Eck, was a mystic who’d gone crazy shortly after construction was completed in the late twenties, and taken his life inside one of the rooms.

After a lengthy Google search, she’d found out that, over the last eighty years, the hotel had seen an unnaturally high number of suicides, several unexplained disappearances, and continuous reports of ghostly phenomena. It was the perfect subject for her next feature article.

Having been built in the twenties, Scarlett had expected a hotel with gravitas; art deco and period decor. Instead, she found a hotel whose character had been stripped away by a series of recent renovations. There were small reminders of the hotel’s history here and there, like the inscription on the stone façade over the front doors, “But take courage; the race of man is divine,” but it was otherwise new, and modern, and sterile. “Might as well be a Holiday Inn,” she thought.

“Was I supposed to go right or straight?” she thought as she stepped off the elevator. The building was a basic rectangle, which she also found disappointing, as she would be able to describe it as neither sprawling nor labyrinthine. “Maybe I’ll have to break out ‘parallelogram,'” she thought. Hallways stretched out straight in front of her and directly to her right.

She looked for a sign to indicate which way was which, but couldn’t find one, so she shook her head and headed down the hall in front of her. Her suitcase was old, and the wheels wobbled, so it made a thunk, thunk, thunk sound as she pulled it behind her.

On the door of each of the rooms was a number superimposed over the hotel’s logo – a motif of a triangle which was composed of ten dots arranged in rows of one, two, three, and four. She frowned and, through a mind clouded by fatigue, tried to recall where she’d seen it before.

Thunk, thunk, thunk. As she plodded down the hall, she remembered seeing the symbol in a Wikipedia article. It was a tetractys – a mystical symbol important to the Pythagoreans.

“Oh, no kidding,” she thought to herself. “Maybe this isn’t going to be a wild goose chase.”

At the end of the hall, she turned right, walked down another hall, and turned right again. Thunk, thunk, thunk. On the wall to her left was one of the infrequent reminders of the hotel’s history: an oil painting of a hunting dog, bordered by a thick, gilded, art-deco frame. “See, that’s more like it,” she thought, and made a mental note to come back and take a picture of it later.

Scarlett stopped for a moment and looked at the room numbers – they were counting down instead of up, in contrast to the two hallways she’d just walked down. “Crap,” she thought, “where the hell is my room?” She kept walking, turned another corner, and looked at the numbers again – now they were counting up. “Weird.”

She turned right again, saw the elevator doors at the end of the hall, and then spotted her room two doors from the elevator – 171. “Figures – I should have gone the other way. Oh well.”

She slipped her keycard in the lock, the light turned green, and she wheeled her bag into the room. Then she yawned again, rubbed her eyes, and headed straight for the bed.

She had just pulled the covers over her head, when her brain finally caught up. “Wait. How many times did you turn the corner?” it asked her.

She sat up and thought through the hallways in her mind, retracing her steps. “Four. I turned four times before I saw the corner where I started. That means that there are five corners total – five right angles. In a rectangle.”

She rubbed her eyes and yawned. “That can’t be right.”

“It’s totally right. You turned the corner four times,” replied her brain.

“No. That’s not possible. I’m just tired. I must have imagined it.”

“You didn’t imagine it. I’m telling you – it was four times.”

“There’s no way. I was up late last night, and it’s late now. I just need to sleep.” She lay back down, closed her eyes, and immediately drifted off.

She was asleep for ten minutes when her brain woke her back up again. “It was four.”

“It can’t be four, brain. Go back to sleep.”

“Fuck you, that’s some weird-ass shit right there. You need to go check it out.”


“I’m not going to let you sleep until you check.”

“Are you serious?”

“Well, I can’t sleep until you look, and if I can’t sleep then you can’t sleep.”

“God damn it.” She sat up, threw off the covers, and shuffled to the door. She stopped and looked at the latch. “Crap,” she thought, “I forgot to lock the door, too.”

“See, aren’t you glad I got you up?”

“Go to hell,” she told her brain as she opened the door.

“You forgot your keycard.”

She turned around and grabbed the card off the nightstand. “Fine. I’m sorry I told you to go to hell.”

“Whatever, don’t get distracted.”

Scarlett looked to her right, down the hall, then to her left, toward the elevators. She decided to start where she’d begun, so she shuffled to the elevators, and then walked down the hall, counting the number of turns she took.

Shuffle, shuffle, shuffle. She noticed that the carpet was woven with a pattern of the triangular logo repeated over and over. In her groggy state, she found staring at it a bit hypnotic. “One,” she said to herself, as she turned the first corner.

Shuffle, shuffle, shuffle. “Two.” She saw the picture of the dog again.

Shuffle, shuffle, shuffle. “Three.” Scarlett expected to see the elevator at the end of the hall when she turned the corner, but instead saw another hall exactly like the one she had just walked down.

“I TOLD YOU!” said her brain.

“What the…” Scarlett thought as she quickly walked to the next corner. She peeked around, and sure enough – there was the elevator at the end of the hall and her room on the left.

She looked back down the hall she’d just come from, then looked back again. “No way.”


“Ok, let’s try this again.” She walked quickly this time: one corner, two corners, dog painting. Three corners, four corners, and then back to the elevator at corner number five.

She ran through the halls. One, two, dog, three, four, elevator, five. “What…the…fuck.”

“I’m just going to shut up now,” her brain said quietly.

Scarlett had been blogging about the paranormal since the heyday of AOL, and she’d seen things that had both scared and scarred her, but she’d rarely felt as discomfited as she did at that moment; goose-bumps ran down her arms and up the back of her neck.

After closing and locking the door to her room, she pulled out her iPhone and called her best friend, a college classmate who had stuck around longer than anyone else in her life.

“Hello?” came the groggy answer.

“Jeff? It’s me, Scarlett.”

“I know. You’re in my phone. That’s why I answered.” He yawned loudly. “What’s wrong?”

“I think I’m in a hypercube.”


“I said I think I’m in a hypercube.”

There was a long pause on the other end of the phone before he replied, “Wasn’t that the name of that horrible sci-fi movie where everyone is trapped in a mysterious prison that keeps changing?”

“Er, yeah, I think so.”

“And they all die in some weird, gruesome way, and in the end it has something to do with time?”

“Well, yeah, although there’s less gruesome dying involved here.” She shivered, involuntarily. “I hope.”

“Why did we watch that again?”

“Well, it was a sequel, and the first one was good, and it was the next thing in my Netflix queue, and never mind that. For real – I think I’m in a hypercube.”

“Are you high right now? Because you sound like you’re high, and it’s twelve-thirty at night, and I have to work in the morning.”

“I’m not high.”

“Are you tripping?”

“No, jerk, I am not tripping.”


“Fuck you, Jeff. I am stone-cold sober. I’m just tired. Or I was until I figured out that the geometry of this building is all screwed up.” She yawned and rubbed her eyes.

“Ok, fine. Then, seriously, what the hell are you talking about?”

She explained the layout of the hotel – the rectangular floor with five right angles, the impossibility of the geometry.

“Huh,” he said after he’d had a moment to think her analysis through.


“Are you sure you’re not on the surface of a sphere?”


“I paid attention in math class, too, you know. Can’t you have a triangle with three right angles on the surface of a sphere?”

“But it’s not a triangle. It’s a rectangle with five sides.”

“Oh, right.” He paused for a few moments, then sighed. “Well, you can’t be the first person to notice it. Did you call the front desk?”

Scarlett was caught off guard by the practicality of the suggestion. “No, of course not,” she sighed to herself, “This is why I call you, you know.”

“Yeah, I know,” he yawned. “Need anything else?”

“No. Thanks, Jeff. I’m going to go see the desk clerk and ask what the holy hell is going on.”

“Let me know how it goes. Oh, also, remember to throw your shoe into any of the rooms first to see if they’re going to kill you. They did that in the movie.”

“I’ll keep that in mind.”

The desk clerk was blond, pretty, and in her mid-thirties. She had her hair pulled up in a bun and wore a crisply pressed suit with a tiny, engraved name tag that read, “Diana.” Like almost everything else in the hotel, Scarlett had thought when she’d checked in earlier, the woman was perfectly modern and somewhat boring.

Now, though, the clerk looked uncomfortable; she smiled with every part of her face but her eyes. “I’m not sure what you’re talking about.”

“The first floor. There are five right angles…five corners at right angles…they make a rectangle, but that’s impossible.”

“I’m sorry, ma’am. I don’t understand.” She glanced nervously at her wristwatch.

“Ok,” Scarlett sighed. “Look, the building is a rectangle, right?”


“Rectangles have four corners and four sides, but there’s a fifth one.”

Diana pursed her lips and sighed, “Well, that clearly can’t be. The building is, as you say, a rectangle.”

“But I know what I saw. I was just up there. Look, I’m a paranormal blogger, and I came to write a story about the guy who designed this place and about the ghost sightings over the years – but this is way bigger. Can I talk to your manager? I’ve got to know what’s going on here.”

“Well, if you check back in the morning,” she glanced at her watch again, “I’m sure my manager would be happy to talk with you.”

“Fine,” Scarlett’s feelings of unease had transformed into excitement at the prospect of landing a major story that had never been covered in the paranormal press, “But I’m going to go take some pictures now and write up a post. You have wi-fi, right? This is going to be huge.”

Diana stiffened. “Wait.”


Diana’s smile faded. “You’re right, of course,” she said as she stepped out from behind the counter. “There is something special about this hotel.” She checked her watch again, “Why don’t you let me show you what you really want to see?”

Scarlett raised an eyebrow. “What’s that?”

“Room 153 – where Paul van Eck killed himself.”

“What does that have to do with the fucked up extra hallway?”

“I’ll explain on the way.”

Scarlett shrugged and motioned to the elevator. “I’m all ears.”

“So how familiar are you with n-dimensional geometry?” asked Diana as she led Scarlett down the hallway.

“I was a math minor in college. Oh my god, is this actually a hypercube?”

“We prefer the term tesseract,” she said curtly as she pressed the button to call the elevator.

“For real?”

“Yes, the building was built in four dimensions. The trouble, of course, is that a four dimensional object is inherently unstable in three dimensions. As it rotates, parts of it project into and out of our world.”

Scarlett’s head swam. She couldn’t grasp how a physically-impossible hotel could have been built nearly eighty years ago and no one had ever found out. She followed Diana into the elevator, and shook her head in disbelief. After a moment, she said, “I can’t have been the first person to figure this out.”

Diana shrugged and gave a half-smile, “Oh, you’re not. It doesn’t happen all that often, though.”

“Why is that?”

“The tesseract was built to rotate in the middle of the night, specifically so that most people would never notice.”

“What about the people staying in those rooms? What happens to them?”

“Well,” she grimaced, “Only one person has ever stayed overnight in a room that rotated…away.”


“It was van Eck. When his room finally rotated back, they found him dead. He’d hung himself from the ceiling fan.”

Scarlett frowned. Something didn’t add up; the hotel had a grisly history – suicides, drug overdoses, and unexplained disappearances. She noticed that Diana kept checking her watch. A chill ran up and down her spine.

“When did you say the hotel rotates, again?”

“Sorry?” The doors opened and Diana stepped out of the elevator. As she did so, Scarlett caught sight of a tattoo on the back of her neck, peeking out from under her collar. It was the triangle logo – the tetractys. “Oh shit,” she thought.

“What happens to the people who are just walking down the hall when it rotates away?”

“Sorry? The room’s just a little farther, now,” Diana said as she walked briskly down the first hall.

Scarlett felt the hair on the back of her neck stand up. “Diana?”

“Quickly, now.” They turned the first corner.

“You said that only one person stayed overnight, but what happens to people who are just walking down the hall?”

“Almost there.” They turned the second corner and entered the hallway with the picture of the dog. Scarlett noticed, for the first time, that doors didn’t have modern electronic locks – they had tarnished brass locks and handles instead.

Diana pulled out a key ring and stopped in front of the door to Room 153. “Here we are.”

“What happens to the people who are walking by? What happens to the people who figure it out?”

Diana opened the door and motioned to Scarlett to enter. “Just go right in and I’ll answer all of your questions.”

Scarlett froze. Her blood ran cold and every part of her being screamed out at her not to step foot in that room. She knew, though she didn’t understand how, that if she went into that room, she would never be seen again.

“After you,” Diana said again.

Scarlett stepped forward, and then, when she was a foot from the door, reached out and pushed Diana in, instead. The clerk tumbled over her own feet and went sprawling on the old, dusty carpet. Scarlett grabbed the handle, and shut the door. She heard the lock click into place.

“No!” Diana yelled. “You stupid bitch! Let me out!”

Scarlett looked down. The key ring was lying on the floor. The handle started to rattle, but Scarlett held it tight.

“Let me out! You have to let me out!” the clerk screamed. She started pounding on the door. “Oh my god, you have to let me out!”

In the distance, Scarlett could hear a clock chime softly, the sound drifting gently through the air above the shouting and pounding and rattling.

“Oh god, No!” Diana yelled again, and the rattling and pounding grew louder. Suddenly, a shrill scream pierced the air, and the noises stopped. Then, the door in front of her started to distort inward, the handle pulling away from her hand.

Scarlett let go and jumped back. She looked to the right and could see the hallway itself stretching and twisting. “Oh, shit!”

She ran, and could feel her body twisting along with the hallway. She had to concentrate to put one foot in front of the next – the stretching threatened to tie her legs into knots. “Oh fuck oh fuck oh fuck!” she screamed as she reached the corner.

With a grunt, she jumped, twisting herself around the corner and landing safely on the carpet of the next hallway. She lay still for a moment, waiting to see if her body was going to twist itself into a pretzel. When that didn’t happen, she pushed herself up, and cautiously approached the corner. She peeked around and saw a perfectly normal hallway – no brass handles, no dog painting.

“Ok,” said her brain, “Time to go.”

“Yep,” she thought. For once, she was in no mood to argue with herself.

“So are you going to write an article about it?” asked Jeff, as they sat at his kitchen table the following afternoon.

After her narrow escape, Scarlett had driven straight home and locked herself in her house, whereupon a healthy dose of bourbon helped put her to sleep.

“Based upon the fact that the creepy Pythagorean cult member tried to get the hotel to eat me when I told her I knew what was going on, I’m thinking no.” She shivered. “I’ve seen some weird shit, man, but I have never had a building try to suck me into another dimension. This is a first.”

“Seems like too good a story to waste, though.”

“I’ll break it out at dinner parties. It’ll be a riot.”

“Well, people already think you’re crazy,” Jeff snorted. “So I don’t think it’s too much of a stretch.”

“Yeah, yeah,” she waved dismissively at him.

“Ok, Scarlett, I’ve got to get ready to go on shift.”

“Oh hey – what are you doing next Saturday?”

“I’ll have to check with Mary, but I don’t think anything. Why?”

“I’ve got a lead on a church in the area that’s supposed to secretly house a holy relic. Want to come with?”

“We have holy relics in Cleveland?”

“Why not? We’re just as religious as anywhere else.”

“This church isn’t going to try to eat me is it?”


He shrugged. “Sure. Sounds like fun.”

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