Milton didn’t know what had gone wrong.

He stared into the depths of his Persian carpet. Intricate, interlocking designs that fused into larger and still larger patterns. The dimensions of the design usually fascinated him, but at the moment, he was consumed by anger.

“Where are you?” he screamed.

He had done everything correctly. He was sure he had. The ancient texts. The modern commentaries. His own analysis. Patterns within patterns. Why wasn’t it working?

Milton let out an exasperated grunt. He took a calming sip of his favorite red wine and set down the glass. In fury, he swept an arm across one side of his well-worn desk, pushing a pile of fragile books and papers onto the floor. He leaned back in his chair, which was cushioned on every surface. It did little to comfort him.

A faint sound. No, more a feeling than a sound. Was someone there? Milton listened intently and looked around him. Nothing. Nothing at all.

He sighed, tapping his lower lip with a bandaged finger as his anger slowly faded. “I don’t know. There isn’t anything else to do. But I must study and try again.”

Milton leaned forward to collect his notes and books from the floor. As he did so, he saw a dark red droplet fall onto the topmost paper.

On top of everything else, I spilled the wine, he thought.

Another droplet landed on his papers. Then another. Then several.

Milton touched his chest. His hand came away wet and red.

He stared in disbelief as he fell forward onto his research.

*     *     *
“The strawberry tart is delicious,” said Molly. “Here, try it.”

Susan took a bite of the dripping pastry. A trail of sticky red liquid ran down her chin as she chewed.

“Oooh, you’re right,” she said. “Messy but delicious.” She wiped her mouth with a cocktail napkin.

Molly surveyed the long table that was larded with sweet and savory foods. Platters of oversized cookies and glistening sliced fruit shared space with fried chicken and a pinkish mound of roast beef. The company took pride in its end-of-summer party, celebrating the year’s software releases.

“How do you like my strawberry tart?” asked a familiar voice. The women turned and saw Harris grinning at them.

“It’s my mother’s famous recipe,” he said. “All the neighborhood kids would find a reason to visit our house whenever my mom made it.”

“You brought that?” said Susan. “It’s the best-tasting item on the table. Our benevolent overlords might get jealous.”

Molly raised a cautionary finger to her lips. “Not too loud. You wouldn’t want to get fired on your birthday.”

Susan blushed. “Molly, you weren’t supposed to tell anyone! You know I’ve reached the age where I hate birthdays.”

“Harris isn’t just anyone. Besides, birthdays are great. I even got you a present.” She turned to a nearby table and retrieved a pale blue package she had stashed behind a pile of technical journals. Atop the package was a decoration made of folded paper, inscribed SUSAN KIM in exuberant capital letters.

“That’s so sweet! Can I open it now? I’m terrible at waiting.”

“Sure. I want to see your reaction.”

Susan removed the intricate decoration and set it aside. She tore off the wrapping paper and dropped it in the wastebasket that was brimming with food-smeared paper plates.

“A scavenger hunt game! I used to love these when I was little.”

“And you play it with your phone. You and your daughter can have a great time with it.”

“I helped pick it out,” said Harris.

“Yes, you looked over my shoulder while I was buying it,” Molly answered.

“And I said I liked it.”

“It looks fun,” said Susan, hoping to end the micro-argument before it escalated. “I can’t wait to play it with Jillian. And I love the decoration you made. What is it?”

She picked up the odd ornament and fingered the edges. It was an irregular polygon with a quirky but appealing asymmetry. Everything balanced visually in the complex array of sharp paper folds. The tactile aspect provided a surprise: although the object appeared to be folded flat, there was a curious thickness to the touch.

Molly’s smile was bittersweet.

“It’s called a lodigarri. My dad showed me how to make them a couple of months ago, not long before … well, you know. I wanted you to have one.”

“Aw, I’m touched,” said Susan. “Milton was a dear. And you are, too. Thank you. What does ‘lodigarri’ mean?”

“I have no idea. I think Dad just made up the word and liked the way it sounded.”

“Can you show me how to fold one? I’d love to learn.”

“You bet. Dad would be pleased.”

Molly pulled out several sheets of printer paper and began to teach her friend the art of folding a lodigarri. Harris watched with patience but without interest.

*     *     *
Susan sat at her desk the following morning, puzzling through her code to figure out why her program had crashed. This will be the bug, she thought. This will be the one I can’t figure out. My career is over.

The rational part of her brain chimed in. Don’t be silly, it said. You always track down the bug in the end. You have a quick mind. Look how fast you learned to fold a lodigarri.

Susan looked at the bright yellow ornament that Molly had given her. It sat on her desk a short distance from her mouse pad, where she could reach out and caress its odd squishiness for comfort. She extended her arm and stroked the folded paper as Molly entered the office.

Molly smiled. “Glad to see you’ve given my dad’s decoration a place of honor. How’d it go with the scavenger hunt game?”

Susan rolled her eyes. “That daughter of mine is scary. Jillian is determined to make me feel slow and old, and she succeeded. I’d found three of the items when she won the game by getting all ten. Have you ever felt proud and embarrassed at the same time?”

“I look forward to that experience when I have my own kids.”

“Oh, it’s a riot. The game really was fun, though. Even if I lost spectacularly.”

“Glad you enjoyed it.”

Susan paused before continuing. “Molly, you don’t have to tell me if you don’t want to, but has there been any more news about what happened to your dad?”

Molly shrugged. “Not a thing. The police think some nutcase came in and stabbed him, hoping to steal something. Dad was bad about leaving the door unlocked.”

“I’m so sorry.” Susan’s hand unconsciously wandered to her lodigarri again.

“You know, Dad had one of those on his desk when he died,” Molly said.

“Really?” Susan pulled her hand back to her mouse pad.

“Yep. I don’t think it was the murder weapon, though. He didn’t die of a paper cut.”

Susan flinched.

“Sorry, bad joke. I’m allowed to make those. God, I loved him.”

Molly walked out of the room and left Susan to her work.

The afternoon faded into evening, then into night. Jillian was at a sleepover with a friend, so Susan could work late without parental guilt. She found her bug, repairing it with delighted enthusiasm. She checked her fix into the codebase and prepared to go home.

Susan picked up the lodigarri from her desk and felt a flash of pain. She looked at her finger.

Paper cut. Ouch.

No one dies of a paper cut. Ha ha.

Susan noted with regret that a droplet of blood from her finger had fallen onto the lodigarri. She tried to wipe it off with a tissue but only succeeded in making the stain larger.

Red and yellow make orange. It’s still beautiful.

She put a bandage on her finger, then put the lodigarri in her purse and left the office. She saw lights in two rooms down the hall and smiled wryly. Molly and Harris were still at work. No kids at home for them to be worried about.

Susan left the building through the deserted side lobby. She was walking across the poorly lit parking lot when she heard a wispy sound. Glancing up, she saw a murky fluorescent light that was sputtering slightly.

She began to walk faster as she pulled out a key ring decorated with a toothy photo of her daughter. As she approached her car, the keys slipped out of her fingers and fell to the asphalt with a clink.

Susan bent over to retrieve her keys. She felt an odd spinning sensation, then blackness.

The keys now had a partner on the pavement.

Susan’s severed head.

*     *     *
“It had to have been done with tremendous force, and with something very sharp,” said the officer. “Did your friend know anyone who collected swords, or something along those lines?”

Molly shook her head. Damned local cop, she thought. He noticed Susan was Asian and assumed she was killed by a samurai wannabe. Brilliant.

The officer seemed to sense he had said something inappropriate.

“I apologize,” he said. “That didn’t come out right. I’m sorry about your friend, but the manner of death is very unusual. Finding the weapon would be enormously helpful, and it’s obviously not here.”

He pointed to the crime scene. Susan’s body had been removed, leaving behind a gruesome wash of blood on the pavement. Her white purse lay nearby, two small red droplets marring its exterior. The top of the purse had come open and Molly could see inside. With a start, she recognized the bloodstained lodigarri atop Susan’s belongings. She closed her eyes with revulsion.

Harris grasped her hand. “May we leave, Officer?” he asked. “There’s nothing else we can tell you.”

The policeman nodded. “We have your contact info. Drive safely.”

Harris and Molly turned away and walked to their car. Harris fumbled for his keys with a shaky hand and started the engine.

They had driven in silence for several minutes when Molly spoke.

“If we hadn’t been working so late, we might have been there when it happened. Maybe we could have stopped it, or at least seen who did it.”

Harris clicked his tongue. “You can’t think like that. Way too much of life is dumb luck. We got lucky and Susan didn’t.”

“It feels too much like my dad all over again. A horrible, bloody murder. No one saw anything. There’s no weapon. No suspects. I can’t stand it.”

“I don’t know what to say.”

“Neither do I. It’s so senseless.”

Silence returned. Harris narrowly dodged an oncoming car that threatened to slew into their lane. He swore.

“See? That could have been our turn. There’s no sense to anything.”

“Maybe we can find some answers,” said Molly. “I haven’t had the heart to go through my dad’s papers yet, but I think it’s time. There might be some reference in there that would be meaningless to others but would have significance for me, or for you.”

“All right. How soon do you want to go?”

“How about now?”

“Please tell me you’re kidding.”

“I’m not. I won’t be able to sleep tonight, so I might as well do something useful.”

Harris dutifully flicked the turn signal and made a left on the road to Milton’s house.

*     *     *
Milton Hawthorne had spent most of his life in an unpretentious mid-century modern home near the university where he had taught. As a professor of anthropology, he had enjoyed living in a house that was once considered dated and stodgy, but was later seen as retro and desirable. He took special pleasure in the ever-shifting customs and tastes of humanity.

As the car pulled into Milton’s driveway, Molly again had to remind herself that the house was now hers. Legally, this was true—her mother had died when Molly was in college—but the house was, and always would be, her father’s. She could never live there herself and dreaded going inside.

Information. Focus on getting information, she thought as she stepped out of the car.

With Harris at her side, Molly unlocked the front door of the house and pulled it open. As she groped for the light switch, she was overwhelmed by the smell. Not the stench of death or murder, but the smell of the house. The smell of her parents. Too many memories. She didn’t know if she could enter.

The hallway light flicked on. Harris put a reassuring arm around Molly’s shoulder and they stepped inside.

They made their way to Milton’s study and turned on the sconces that illuminated the room. It was never very bright in the study, which was how the professor had liked it. Atop his massive walnut desk, his papers were piled with surprising neatness. The police had made an effort to return everything in reasonably good order after completing their investigation.

Molly sat down in her father’s padded armchair. Harris dragged a smaller chair across the Persian carpet to face Molly across the desk.

“What are we looking for?” asked Harris.

“Anything weird. Or especially weird, I guess. Dad was fascinated with a lot of strange stuff.”

They divided the papers and dove in.

An hour passed. Harris frequently squinted or put his fingers to his temples as he read through the professor’s cryptic notes.

Molly opened the next notebook in her pile and frowned.

“What’s wrong?” asked Harris.

“This is math,” Molly said. “Calculus. That’s an integral sign.”

Harris looked at the page and groaned. “Good Lord, you’re right. I failed calculus. Integral signs still haunt my nightmares.”

“Why was Dad interested in this stuff? He was an anthropologist. He was good at math but rarely used it.”

Molly turned the page. Under a swirl of increasingly messy calculations was a command: “Ask Bartletti.”

Harris swore quietly. Molly looked at him with raised eyebrows.

“Do you know who that is?”

“Given that it’s math, your dad was probably talking about Professor Bartletti at the university. Giacomo Bartletti. He’s the teacher who flunked me in calculus.”

Molly picked up the notebook and snapped it shut.

“We’ll need to meet with him. Prepare yourself. I don’t think we can do any more tonight.”

*     *     *
Prof. Bartletti welcomed the visitors into his office. The professor was a rotund man of advanced age who had worn a small goatee since his days in graduate school. Like Milton’s mid-century modern house, the beard had gone from popular to dated to retro chic. Unlike the anthropologist, Prof. Bartletti didn’t care.

“I was very sorry to hear about your father, Ms. Hawthorne,” he said. “Milton was a kind and fascinating man with an original mind.”

“Thank you, professor,” said Molly. “As I told you on the phone, we’re here because Dad mentioned you in one of his notebooks. It looks like he got stuck on a bit of math.” She produced the notebook and handed it to Bartletti.

The professor studied the equations and tipped his head to one side.

“This is impressive. Your father was better at mathematics than he liked to admit. I myself have done a good amount of work in topological ambiguity and Milton was very interested in that.”

“Why?” asked Molly.

“Do you know anything about differential topology?” Bartletti’s eyes shifted to Harris. “I know you don’t, Mr. Lombard.”

“Well, I bet you don’t know who won the NCAA championship this year,” Harris answered.

“The NCCA championship doesn’t have anything to do with this.”

“I knew it,” Harris said with a smirk.

The professor had already turned his attention back to Molly.

“The final conversation I had with your father was disquieting. He asked me not to repeat it, but I don’t see any harm in doing so now. It surely didn’t have anything to do with his death, but it involved an intellectually questionable endeavor he was pursuing.”

“Go on.”

Bartletti blinked slowly. “Milton expressed a belief in higher dimensions and wanted to know if I thought they were mathematically possible.”

Harris cut in. “You mean like religion?”

The professor gave him an irritated look. “No, young man. Physical dimensions.”

“But I thought time was the fourth dimension,” Harris continued.

“I’m pleasantly surprised you know that, Mr. Lombard, but time is Einstein’s fourth dimension. Milton and I were talking about higher dimensions in conventional Euclidian space.”

“You lost me,” said Harris.

“Of course I did.”

Molly spoke up. “You mean a fourth dimension that’s perpendicular to all our dimensions here in the normal world.”

The professor beamed. “Exactly. It has always been a subject of speculation, but no one has ever produced evidence for more than three dimensions. I told Milton it was theoretically possible but profoundly unlikely.”

“Why was Dad interested in such a strange topic?”

“He said he’d run across references to higher dimensions in writings from several different cultures, and he believed there was something to it. He was particularly interested in an old Basque legend about a talisman that could thicken three dimensions into four. The talisman was a topologically ambiguous object called a locomotive, or something like that.”

Molly gasped. “Lodigarri?”

“Yes, that sounds right. I’d never heard the term before. Milton was interested in the mathematics of such an object.”

“All that calculus.”

Bartletti made a dismissive gesture. “He was going on and on about higher-dimensional entities coexisting with us. Dimensions within dimensions. Patterns within patterns. I don’t mean to speak ill of your father, but it was both bizarre and boring. A curious combination.”

“I have a lodigarri right here.”

Molly reached into her purse and began to pull out the lodigarri she carried with her. It snagged a corner of her wallet and the paper slipped sideways, cutting her finger. She cried out as a drop of her blood fell into its folds.

Bartletti looked across his immaculate desk. “Do you require a bandage?”

Molly shook her head while extracting a Band-Aid from her wallet. She quickly secured the adhesive, then held up the lodigarri between two fingers.

The professor looked at the paper with distaste.

“Forgive me for not wanting to examine your soggy origami, Ms. Hawthorne. But I do hope it provides you with happy memories of your father.”

Molly put the lodigarri back into her purse and stood up. Harris joined her.

“Thank you very much for your time, professor,” Molly said.

“And you might try looking up ‘NCAA,’” Harris added.

*     *     *
The ride home was uncomfortable.

“So please don’t tell me you think Susan and your dad were killed by interdimensional creatures from another planet,” said Harris.

“Not from another planet, no.”

“Interdimensional creatures from Earth, then? Maybe Cleveland?”

Molly sighed. “It doesn’t work that way. Or it wouldn’t, if things like that were real. I don’t know what to think. It sounds nutty but Dad was a brilliant man.”

“But he was interested in weird stuff. You said that yourself.”

“Weird isn’t crazy.”

“Sometimes it is. Especially when you’re talking about monsters from another dimension.”

“He wouldn’t have seen them as monsters. They would simply have been another culture for him to study.”

Harris threw up his hands, then quickly placed them back on the steering wheel. Conversation stopped.

Molly began to cry quietly.

“The lodigarri is tainted for me now,” she said. “It was one of the last things I learned from Dad, and it was a beautiful memory. Now it’s either a piece of crackpot nonsense or something that killed two people.”

“It didn’t kill anyone,” said Harris.

“Both Dad and Susan had one with them when they died.”

“And they were both wearing clothes, and they both drank water on the day they were killed. Correlation is not causation.”

Susan’s anger stopped her tears. “Don’t you think I know that? You pick the worst times to be intelligent.”

Harris took a moment to consider his answer. “I’m sorry. I just can’t believe that a piece of origami can open the door to bloodthirsty creatures from the fourth dimension.”

“Bloodthirsty. Blood. Oh my God.”

“Hey, I said I’m sorry.”

“No, no. I see it now. Paper cuts. Opening the door.”

“You’re gonna have to spell that out for me.”

Molly’s face was pale. “The lodigarris near the bodies had blood on them.”

“Is that surprising?”

“Yes. Dad fell onto the floor, but the lodigarri was on the far corner of his desk. And Susan’s was inside her purse where there was hardly any blood.”

“Okay. Why is that significant?”

“Both Susan and Dad had bandages on their fingers. Like this.” She held up her own injured finger.

“Irritating but hardly fatal.”

“I think the lodigarri is designed to inflict paper cuts with its sharp edges. And it’s hungry. Without blood, it’s harmless.”

“I admit you’re creeping me out, but that sounds like complete drivel.”

“Maybe. I hope so. At least I’m still alive.”

Harris pulled the car into their driveway. Molly got out and slammed the door. She stood still, concentrating intently.

“Do you hear that? Sort of a gentle whooshing sound.”

Harris listened. “Nope. Nothing.”

Molly raised her arm in front of her face in a defensive posture and moved forward slowly. She screamed.

A bright crimson line appeared on her forearm. It dripped blood onto the asphalt.

“Get back in the car!” yelled Harris.

Her body shaking, Molly retreated.

*     *     *
The young doctor in the emergency room stitched up the ugly wound in Molly’s arm with brisk professionalism. Molly showed no reaction to the procedure as she lay quietly on the paper-draped hospital table, staring into the air. Harris sat in an uncomfortable chair nearby, looking at Molly with concern but remaining silent.

The doctor cleared his throat. “Okay, that will do it. You’re sure you can’t provide a description of the person who did this to you?” His eyes shifted to Harris and back to Molly.

“It happened too fast,” said Molly. “And for God’s sake, it wasn’t my husband. I know you must see a lot of domestic violence in here, but Harris isn’t like that.”

“Okay, I’m sorry,” said the physician, flicking an imaginary piece of dust from his blue scrubs. “Can you tell me anything about the weapon? The wound was made with a very sharp blade.”

“No idea. One minute, I was fine. The next, my arm was leaking blood. That’s all.”

Harris added an unhelpful shrug of his own.

The doctor frowned. “All right. Your arm should heal well, unless you run into the same mysterious person again. I suggest you file a police report. Good luck to you.” He left the room.

Harris helped Molly off the table. She raised her forearm in front of her face as they walked back to the waiting area.

“Sit here,” Harris said. “I’ll be back in a few minutes.”

Molly sat and tried to think. The whole thing would be ridiculous if it weren’t terrifying.

Harris returned shortly with something in a long paper bag. He grinned as he pulled out his purchase.

“Voilà! The biggest baguette the bakery had. Hold it in front of you and stop chancing your arm.”

Molly took the baguette and smiled. She arose and left the emergency room with Harris, her protective baguette pointing ahead like a large and crusty magic wand.

*     *     *
Harris was snoring.

His head lay against Molly’s shoulder as they snuggled together on the leather couch in their living room. Molly rested her injured arm on the padded armrest, her still-undamaged baguette within easy reach. There had been no hint of danger on the journey home.

What was happening? Something unseen had slashed her arm, and it was probably the same thing that had killed her father and Susan. Could it really be connected to the lodigarri? It seemed like a deranged fairy tale or a tabloid headline.

So where was the fourth dimension her father had sought? Why didn’t she have some perception of it herself, if the lodigarri worked as advertised? According to that old Basque legend, the ornament was supposed to thicken three dimensions into four. But Molly was still as three-dimensional as ever, and she was being attacked by an instrument so razor-thin it barely made it into three dimensions, much less four.

It came to her in a thunderclap.

The lodigarri didn’t thicken three dimensions into four. It thickened two dimensions into three.

Two-dimensional creatures. Why not? At least she had no trouble visualizing two dimensions. Such entities would have no thickness and could well be imperceptible in the 3D world. The creatures would think of a third dimension in much the same way as humans thought of a fourth one: theoretically possible but mentally unfathomable.

What would happen if such a creature were suddenly granted a dimension of thickness, through a topologically ambiguous talisman and a blood ritual?

Terror. Disorientation. Insanity.

And perhaps a physical bond to the human whose blood had torn the fabric of its reality.

There was a faint whooshing noise. Molly recognized the sound. She grabbed her baguette, waking Harris in the process.

“What’s going on?” he asked.

“I think I’ve figured it out,” Molly answered. “It’s not trying to hurt me. It’s just scared out of its mind and trying to hide.”

“What are you talking about?”

Molly thrust the baguette forward. Something sliced off the tip, which fell to the floor.

“It’s here now. It’s not four-dimensional. It’s a two-dimensional creature that the lodigarri has made 3D, barely.”

“Aha, like the world’s sharpest knife.”

“Okay, now you’re being intelligent at the right time. Yes.”

“So what do we do?”

“It’s my blood that brought it here, so I’m the only one who can interact with it in 3D. It’s bound to me but is incapable of grasping what I am, so it keeps turning that crazily thin edge toward me in an effort to conceal itself.”

“Again, what do we do?”

“Trust me and do exactly what I say.”

Molly reached into her purse on the side table and withdrew the lodigarri. She lifted Harris’s hand, pressed his index finger against one of the sharp paper edges, and pulled the talisman sharply to one side.

“Ouch!”

A drop of Harris’s blood fell from his cut finger into the lodigarri.

“Now it’s bound to both of us, so you’re also in danger,” said Molly. “But it can’t hide from two of us at the same time.”

The wobbly swooshing sound was louder now.

“Lie down on the couch,” ordered Molly. “I need to stand up.”

Gripping her baguette, she arose with great care and walked along the edge of the Persian rug that covered the floor. The bread remained intact, suffering no further injury.

The noise grew even louder, almost into a wail.

Molly saw it.

A vague rectangle suffused with faint iridescent colors, tilting and jittering as if caught in an unseen wind. As it rotated, Molly’s view became clearer.

A face? No, not a face. Pareidolia at work. But something. Something alive and intelligent and horrified. The colors intensified and became more agitated.

I wonder how I look to it, Molly thought.

No answer from the creature. Instead, it began to drift toward the couch, its impossibly sharp edge aimed directly at Harris.

“What’s going on? I don’t see anything,” Harris said.

It was time. Molly didn’t even like stepping on ants, but she had to protect Harris. She lifted the baguette and brought it down as hard as she could on the exposed surface of the creature, away from the edge.

There was a shriek. Harris covered his ears.

Countless tiny fragments swirled in the air, prisms refracting light as they shriveled away.

Then there was nothing.

Molly looked at Harris. “We have to burn everything. My lodigarri. Susan’s as well. Dad’s research notes. The door must be closed.”

“Do you think there are other creatures like that one?”

“I have no plans to find out.”

Harris nodded as Molly pushed her lodigarri into the trash with the edge of her baguette.

*     *     *
A cool autumn breeze blew through the classroom windows, making Ms. Carson smile.

She loved these crisp September mornings with her rows of fourth graders arrayed in front of her. Some were looking up expectantly, others dutifully, and some in outright boredom, but there were always a few students who loved learning. The quiet girl in the first row was one of them.

Ms. Carson clapped her hands to get the class’s attention.

“Good morning! Let’s start the day off in a fun way, with show and tell. Who brought something they’d like to show the class?”

The quiet girl raised her hand.

“Jillian! Certainly. We are very glad to have you back in class with us.”

Jillian rose from her seat and walked the short distance to the front of the room. She held up an intriguing object in her right hand and began to speak.

“I’d like to show you something that’s really important to me. It’s the last thing my mom ever taught me how to do.”

The students craned their necks with interest.

“It’s called a lodigarri,” said Jillian. “I’ll show you how to make one.”