#truncated cube

[knotty-et-al]

Drawing a truncated cube and a cuboctahedron from a cube....

As for understanding truncation: You can imagine having a cheese cube and just cutting of the vertices...

- - -- --- -----

Truncated cubes and cuboctahedra are Archimedian solids.

----- --- -- - -

I used isometric dot paper.

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 1

Propaganda

Icosidodecahedron:

Archimedean Solid

Quasiregular

Dual of the Rhombic Triacontahedron

It has 12 regular pentagonal faces, 20 regular trianglar faces, 60 edges, and 30 vertices.

Vertex Transitive AND Edge Transitive

Image Credit: Cyp

Truncated Cube:

Also called the Truncated Hexahedron

Archimedean Solid

Semiregular

Dual of the Triakis Octahedron

It has 6 regular octagonal faces, 8 regular triangular faces, 36 edges, and 24 vertices.

Image Credit: Cyp

[art-of-mathematics]

(Saaaadly, the Catalan solids dont look that nice in that isometric projection.

Perhaps their charm would become more present if I put shading into these drawings.)

Today's polyhedron drawing is the Triakis Octahedron, which is the dual of the Archimedean solid called "truncated cube".

A triakis octahedron is like an octahedron with 8 triangular pyramid hats.)

Triakis is greek and meens "trice/three times"

A Triakis octahedron has 32 faces: three times eight (octa) - It has the amount of faces as its name.

Each of the 8 triangular faces of the octahedron has a triangular pyramid hat: each of these pyramids has 3 faces, hence 3*8.

That's why it's called "Triakis octahedron"

[queersrus]

hii !!! can i req some names similar to Axe ?

assuming weapon names

hatchet, hack, hash, hew, hackle, hudson, hewing, hunter, haft, halberd, hurlbat, hache, hacha, hak

cleaver, cleave, chop, clip, carve, chip, cube, chopper, cut, cutter, carpenter, crash, climb, climber, cirvis

adze, archer, aizkora, ascia, axt, ak

mince

dice, dayton, daggar/dagger, dane, destral

slash, stab, sever, strike, shear, split, Shepard/Shephard, spontoon, slater, sepate, siakiera, sjekira, sekera, sokyra, securis

whack

lop, lathe/lath, lathing

truncate, tomahawk, tactile, tacticle, tactic, throw, tsekoúri, tuagh, topor

fell, felling, forest, frankish, fancisca, fire, firefighter, fejsze

grub

mattock, maul, miner, mort, mortis/mortise, mortising, machado, mannara

bay, broad, battle, bit, bradva, bijl, bile, bwyell, badrick

pick, pole, pulaski

roof, roofing

ice

okse, oxi, oks

kirves, kirvis

yxa

[sorrelce]

Ok, so my eyes are not great. Wondering if anyone else noticed/can confirm what I'm seeing? The cool team leader badges they made for purgatory....do you think those are designed with intent?

I can't unsee it, but red team the black backing shadow looks like Phil's clipped wings.....

HUH

Any chance a tubbling or someone can grab a better shot of the blue badge? The bg of global chat is not doing me any favors. It looks pretty bland....

Like, Etoiles has a kind of wonky looking thing. The metal band seems to be wrapped/bend around the shadow diamond/cube as if it's a 3d object. I thought at first it was just truncated prongs, but the other two are both closed bands, and the lighting on the silver does seem like it's tilted.

I'm wondering if it was a cool extra hype detail, that they predicted who was likely to be declared leader and made personalized badges for those picks. And Tubbo was a dark horse candidate so he got the 'base' design.

Or if its lore/hints. And Blue's is intentionally bland to draw attention to the fact that there is something funky going on with the other (two). Would red team always have the wings, not because of who their leader is, but because of their roster? Phil, Baghera, Jaiden? What concept is green's hinting at?

Because honestly standard play for differentiation: the rbg split, unique badge shape (silver), and gem cut would honestly be plenty to make them visually distinct.

Why the need to get esoteric with it and start rotating objects and messing with shadow forms???? (Besides cool points, which they win)

[robotblues]

A Space-Filling Pair of Polyhedra: The Cuboctahedron and the Octahedron There are only a few polyhedra which can fill space without leaving gaps, without “help” from a second polyhedron. This filling of space is the three-dimensional version of tessellating a plane. Among those that can do this are the cube, the truncated octahedron, and the rhombic dodecahedron. If multiple polyhedra are allowed in a space-filling pattern, this opens new possibilities. Here is one: the filling of space by cuboctahedra and octahedra. There are others, and they are likely to appear as future blog-posts here. Software credit: I made this virtual model using Stella 4d, polyhedral-manipulation software you can buy, or try as a free trial download, at http://www.software3d.com/Stella.php.

[yaboyyjay]

WATERFALL

Bryce (username: Mario) was listening to music when he received an invitation from his friend, Alexia (username: Cherry), to meet in full dive virtual reality.

Mario didn’t have anything else to do that evening, so he activated his wearable head-mounted display. Then, he paired the wireless, non-invasive input controller (or brain-computer interface) to the display, put it on his head, pulled it down over his eyes, and accepted the invitation.

He was standing in a full-scale model of M.C. Escher’s Waterfall, which had been rendered in a video game engine known for its stunning graphics that pushed the boundaries of VR without any performance issues.

He switched to continuous movement and—using the BCI controller—proceeded up a flight of stairs to examine the impossible machine from below. With an uncapped framerate, silky smooth sparkling water poured over the wood-textured wheel of the watermill. From a traditional perspective, water appeared to zigzag up two tribars and tumble down again—violating the laws of physics.

Bored but unwilling to leave, a few regular users in customized avatars were hanging out on the narrow, shallow, 20th century brick-mapped water channels. Others were leaping from truncated paths and searching for glitches.

Everything else was normal: a non-playable character stood on the flat roof of her home, calmly hanging laundry out to dry, while another NPC—the miller—gazed into the sky. Both seemed oblivious to the impossible waterfall, though they were programmed to comment extensively on the piece.

“Mario!” Cherry greeted from a balcony. Her avatar waved. Mario returned the wave, distracted by what appeared to be a cluster of moss and lichen, enlarged many orders of magnitude and swaying in the breeze.

He craned his neck, eye-trackers tracking his pupils to view two towering supports for the waterfall’s aqueduct. They were topped by two compound polyhedra: three intersecting cubes for one tower and three octahedrons for the other.

Seeing the shapes for the first time triggered an NPC: “Escher loved mathematics and art!” said the woman airing out laundry in an infinite loop.

“Newbie alert!” A regular yelled before leaping from a ledge.

Mario imagined scaling a pillar of the first and highest tower to view the solids. It would be tricky and he wanted to record the geometric wonders.

One problem: Waterfall’s developer had disabled recording. So Mario had to use a different recorder—one that wasn’t on the blocklist.

Mario left Waterfall and joined a sea of avatars in Google’s sprawling search engine. He was using Cherry’s theme, who’d customized everything to look like something out of Tron: a classic film from the Old World with an aesthetic of space, with structures representing social networks scattered across the virtual landscape.

Billions were in the flow of browsing. Mario pulled up a list of stores, then followed directions in his heads-up display to Daydream View, a store selling recorders that bypassed most blocks.

He was auto-greeted by the mascot of Daydream View. With a powerful search engine, it answered most questions before anyone could finish asking them. Except for a few visitors browsing VR video game recorders and other expensive items, the store was all but empty.

After several minutes of browsing, Mario downloaded a VeeVue Recorder and Editor for 20 credits. Then he exited into organized chaos to make his way back to Waterfall; into a world of ads, bots, and users with custom avatars. He didn’t feel like walking so he switched to top-down view, which presented every site from above, then selected Waterfall before diving back into his avatar.

He spawned in with an unrecognizable device that may or may not have been a recorder. Cherry was gone but the site retained a steady stream of visitors coming and going insofar as the mental cost was low.

Mario examined the machine. The aqueduct, which started at the waterwheel, flowed endlessly behind it.

From where he was standing the illusion was broken: directly overhead were ledges of the two tribars. Water flow stopped at each ledge. The bottommost aqueduct formed an L, the middle a Z-like shape, while the uppermost aqueduct was a ledge from which water tumbled down unto the wheel. He shifted his gaze to a curl-up lounging under an arch of a small bridge, which connected the flat roof of a house to the watermill.

A fictional animal invented by Escher, it was programmed to watch Mario with two stalked, beady eyes, then—true to its name—curl up and roll around the villa and climbing expanse of terraced farmland.

“The curl-up is elongated and armored with several keratinized joints,” described the miller. “It has six legs, each with what appears to be a human foot. It has a disc-shaped head with a parrot-like beak and eyes on stalks on either side. It can either crawl over a variety of terrain with its six legs or press its beak to the ground and roll into a wheel shape.”

Mario wondered who was watching. Waterfall’s developer logged every event “to help improve the experience”, which involved tracking users to determine their interests. He suspected Waterfall’s developer would sell his information to businesses, who’d spam his inbox with advertisments.

Nevertheless, he wanted to record everything. It’ll be worth something to someone, he thought. But that wasn’t the only reason he wanted the video. There was also the satisfaction of bypassing obstacles to make it. ThreeVee, the internet’s largest VR video-sharing site, needed a video of Escher’s Waterfall, and Mario wanted to deliver.

_______

Mario spawned at the bottom of a stairwell; an entry to the quaint villa. At the top of the steps was an open space. Behind him, to his right was the home with a large balcony, where the woman was hanging clothes. To his left were some steps descending unto a rooftop, where the miller stood with his back against a railing.

He changed into his favorite parkour outfit and took a deep breath from muscle memory. He wasn’t going to actually run. Instead, he would activate the neurons that triggered locomotion by thinking about running, while the BCI controller translated neuronal signals to movement in VR.

Without hesitation he opened VeeVue and began recording.

________

Mario is gazing up at the waterfall in first person.

From his perspective, the environment blurs as he inhales, sprints, and jump-kicks off a brown painted wall. Then he twists in mid-air to grab the ledge of a small arched walkway serving as a bridge to the mill.

Both of his arms are extending into the field of view, gloved hands gripping the bridge. He hangs for a beat before climbing with his heart rate, then stands to record the top of the walkway.

A trio of regulars are sitting on the only steps to the bottom water channel. One of them glares at Mario and flashes an obscene emote.

“Nice recorder, newbie. How much did you pay for it?”

But Mario jumps over them, splash landing in the channel.

"Hey—!

He breaks into a sprint, aqua blue water sloshing around red running shoes. The brain-reading technology is controlling every step as he stops at the L channel’s drop and whirls 180 degrees, spinning the colorful environment.

Jumping vertically, he grabs the ledge of the second level water channel and pulls himself up.

Then he's free-running the waterway. As he turns a hard corner, the highest tower looms.

Keep running.

He cat-leaps to grab the uppermost ledge with one hand only to slip and splashdown flat, submerging briefly. Two regulars peer over the top ledge and laugh as he springs up gasping for air, overwhelmed by the fear of drowning.

He looks above them: part of the simulated sun is occluded by Escher’s compound of intersecting cubes.

“Mario?”

He’s glancing over the side of the channel to get a bird’s eye view of Cherry’s avatar.

“Up here!” Their eyes meet as he leans slightly over the ledge to flash a victory sign.

“Are you using a recorder?” she tut-tuts. “Those are—”

“No,” Mario lies. He’s backing up to the first corner of the second level water channel.

“Haha,” sneers one of the regulars. “10 credits says he’ll fall again.”

But Mario is running, the sound of his footsteps breaking the surface tension of the water. He gathers speed and leaps, this time catching the ledge with both hands. Inhale.

Exhale.

He pulls himself into a sitting position and the regulars vanish, exiting in unison.

“Pay up!” Mario announces.

But they're gone and he's laughing over the trickle of the waterfall, the birds perched at the height of the tower, and the gentle breeze taken from stock sound clips starting at two credits each.

_______

The top level was supported by four columns that were covered in graffiti tags. Mario would’ve had to shimmy up a column to reach the highest point of the fall.

But balancing on the top level, against the flow, had taken more brain power than he’d expected. He stumbled while reaching for a column, the horizon tilting at a dizzying angle until he fell down the fall, the recorder capturing it all.

“Oof!”

He laid there for a moment, then pulled himself up from where the wheel-powered aqueduct began.

“Ouch...” Cherry said as he exited the channel and vaulted over the railing some three meters to the ground, where several visitors had gathered.

“Did you tag a column?”

“How much fall damage did that take?”

“Waterfall is a lithograph by the Dutch artist M. C. Escher,” the miller said abruptly. “First printed in October 1961. It shows a perpetual motion machine where water from the base of—”

“Skip intro!” Three or four visitors shouted at once.

Mario stopped recording. Paranoid, he glanced around for a moderator that would boot him if they detected a Daydream recorder which, while recording, had changed his avatar’s eyes from a custom color to bright crimson red.

The small crowd of visitors and regulars dwindled with their curiosity. Cherry’s avatar was sitting lotus style in front of Escher’s moss and lichen garden. She could’ve been doing anything from talking to friends to paying off owed credit. Either way, she was absent, and would likely remain so until kicked off the site for going idle.

Mario walked close enough to her avatar for a message to pop up: “Switch to this outfit?” He agreed and was instantly clothed in the same getup configured for male avatars.

He wore a casual, lightweight, sleeveless, slim fit zip-up hoodie over a vantablack printed teeshirt bearing a single, stylized word in hex color red: “CyberPunk”.

Ironically advertising the subculture, the teeshirt hung over a pair of techwear: on-brand harem pants hiked up to his knees and covered with cyberpunk flair.

Dangling before the teeshirt were three necklaces: RGB colored microcircuit boards attached to a thin chain. They’d clink together as he walked, his hands covered in fingerless leather gloves.

“Decent outfit.” Mario said to Cherry’s blank avatar. She’d muted her eye trackers.

_______

Mario decided he’d recorded enough. Falling made him want to try again, but first he wanted to upload his run to ThreeVee.

He stepped back into the infinitely branching traffic of Google, joining the flow once more—billions of avatars travelling at different rates. Some walking, some running, many zipping around on light cycles.

The entire place was alive; the search engine, an organism. Social networks were represented as complex superstructures. Facebook and Twitter towered higher than the graphics engine could render.

“Amazing, huh?” Cherry spawned beside him, exiting Waterfall. She’d changed outfits.

“Yeah, for a walking simulator,” Mario replied. “How is it practical to travel this way?”

Like Cherry, Mario was using the free version of the Tron theme. Light cycles were included in the premium version, although they were cosmetic and wouldn’t travel any faster than what he’d paid for.

“I like it,” she opined. “Makes it more immersive.”

Mario received a notification but ignored it, breaking into a sprint.

Cherry did the same, closing the gap immediately. Browsing at faster speeds, she’d outrun him if she knew where he was going.

“What’s the hurry?” She glided next to Mario, running in parallel. She could see her legs and feet. Her legs were covered in bionic leggings, white, black, and gray, with just a hint of red, detailing metal joints, pistons and other industrial artifacts. Her feet were covered in glow-laced running shoes, each step leaving a digital footprint that could be identified and traced.

“The video of the climb and fall,” he said finally. “If it goes viral, maybe businesses will want to sponsor the content.”

Another notification. This time Mario checked the sender. It was an advertisement for a smart car: autonomous, with maximum communication capabilities, friendly, personalizable and, of course, electric.

Mario deleted the message. Yet the first one went unnoticed as he continued sprinting with traffic towards ThreeVee, represented as a megasize movie theater. It was a tronesque megastructure, with sharply angled architecture and searchlights waving across the digital sky: a landmark surrounded by hundreds of competitors.

But before he could get there Cherry received a notification. She checked it and stopped in the middle of traffic, hundreds of avatars zipping by or walking around her automatically.

“Wait, Mario!” Cherry yelled. Yet Mario continued on, sprinting past Bandcamp’s band camps and through popup ads for channels on YouTube. Then he stopped at ThreeVee and scattered the floating multishaped iterations that had taken an interest in him.

Tracking bots.

“What part of Do Not Track don’t you understand?” Mario yelled at the bots. Many of them scattered, while others merely evaded his swats and returned to their orbits.

On cue, an ad splashed across his visor to upgrade the Tron theme: “No More Tracking Bots,” standing out in bold electric green. For a few credits a day, he could have access to premium features including light cycles and a dozen other abstract modes of transportation.

The recommendation popped up frequently in the free version, but this time he decided to upgrade. His surroundings immediately shifted to the highest possible resolution.

Fetching a bright, electric green baton from his harem pants, he transitioned into a light cycle; a 5th generation personal transport bike. Using a few basic mental commands, he beelined away from ThreeVee, merging with traffic to track Cherry’s footprints.

________

The light cycle may have been a cosmetic upgrade for browsing, but handling one was an out-of-orbit experience.

Using the BCI controller, Mario increased the speed of the vehicle by pushing its front and rear ends further apart. The front wheel was locked forward, so steering was done by tilting the entire bike. When attempting certain maneuvers, a pair of small fins would spring out just behind the vehicle to aid either balance or braking.

A throwback forward, it was a ride worth every credit.

Cherry’s footprints became more vibrant until they stopped at Waterfall. As Mario rode the bike into the site, vanishing in a spark of electric blue light, he remembered the unchecked notification winking in his heads-up display.

_______

Waterfall was crowded with visitors.

Mario skipped up the steps and looked around for Cherry. Then, he opened the newest notification to read its message, noticing that the one he'd ignored was from Waterfall.

“Hey,” it was Cherry. “Did you get a notification from Waterfall?”

“Yeah,” Mario replied, switching to live chat. “Thought it was spam.”

Cherry appeared in the top right corner of his heads-up display. “Where are you? There are too many users outside.”

“What’s going on?” He looked over the crowd. Visitors were walking, running, and climbing ledges to reach the top ledge, where the water fell.

“Meet me inside the Laundry Lady’s house,” she replied.

Weaving through visitors, Mario slipped through the door, entering Escher’s House of Stairs with a start.

_______

“Whoa,” was all he could manage when greeted by the home’s surreal interior. He’d never seen anything like it: upside-down and rightside-up staircases ascending and descending to doorways. More than 40 curl-ups crawling the stairs and rolling around, coming and going through one of more than a dozen open entrances and exits.

Cherry was straddling the carapace of a curl-up that was clipping into a wall—a glitch likely caused by the influx of activity. Other curl-ups followed their program, doing what Escher had imagined.

It was an impressive and logic-defying masterpiece and, except for the strange ticking sound made by walking curl-ups, it was quiet.

“What’s up?” said Mario, still perplexed by the home’s interior. “Why’d you come back here?”

“Check your messeges,” she replied.

Mario opened his inbox and was greeted with Waterfall’s Terms of Service.

“These Terms of Service govern your access to and use of Waterfall.” Mario read aloud.

“By submitting, posting or displaying content on or through Waterfall, you grant us a worldwide, non-exclusive, royalty-free license (with the right to sublicense) to use, copy, reproduce such content in any and all media or distribution methods now known or later developed. This license authorizes us to make your content available to the rest of the world and to let others do the same. You agree—”

Mario shook his head. He didn’t remember agreeing with anything.

“I never—” he started.

“Keep reading,” Cherry urged.

He continued to read, some parts to himself, other parts aloud.

“...that this license includes the right for Waterfall to provide, promote, and improve Waterfall and blah blah blah...”

His eyes glazed over until he read, “...such additional uses by Waterfall is made with no compensation paid to you with respect to the content that you submit through Waterfall as the use of Waterfall by you is hereby agreed—”

A curl-up bowled by Mario, almost knocking him off a ledge.

“...as being sufficient compensation for the content and grant of rights herein.” He finished.

“So...what does this mean?” But Mario knew what it meant before Cherry could rejoin with, “There should be a video attached. Watch it.”

Hesitantly, he checked and saw that his video had been included in the latest advertisement for Waterfall. A video he was being compensated for merely by using the site.

The video had been edited, but much of it was there: his view of the regular flashing an obscene emote while calling him out for using VeeVue. The view of his first unsuccessful cat-leap to the highest ledge, which made him gasp for air. Laughter and mockery from regulars. The bet that he’d fail again.

Then, the fall. Mario stopped the video.

“Wow...” He said, preparing a response. But Cherry hopped off the sunset orange curl-up.

“Yes, they stole your video—” She began.

“They stole my video...” Mario repeated in dismay.

“Yes.” Cherry said. “But check outside. You’re popular!”

Mario was confused until a few visitors entered the house and looked in his direction.

“Hey! It’s him!” One of them said.

“That was an good run,” said another. “Where’d you get those parkour gloves?”

And another: “I recently installed a new BCI controller. How long before I’ll be able to jump like that?”

_______

Mario wasn’t sure how to respond. Being new to the full dive VR experience, he’d assumed less about his mental ability to get around.

"I, uh, fetched the gloves from Precision,” he started to answer. He then realized why they were impressed: training a brain input controller was a difficult process. The advertisement had embarrassed him, but it also showed prospective visitors his ability to move through virtual space using a controller.

It turned out Mario’s ability had taken most visitors some time to imitate, the majority failing the first jump-kick for need of more practice.

“How do I get out of this place?” Mario looked around, confused.

“Take an upside-down left over there,” Cherry pointed in a vague direction.

He spun around while she laughed.

“Dork. You get out the same way you came in”.

Another curl-up rolled by him. This time he stepped out of the way of its path-finding program.

“Precision?” The visitor remarked. “Their gear’s priced higher than space junk!”

“You’re just poor!”

They argued as Mario exited to the waterfall, where visitors seemed to have doubled in size. He looked over the crowd. Newbies were awkwardly climbing, falling, and running about practicing with their BCIs.

He’d started a trend. One he needed a clue to promote.

“Hey!” Someone said, pointing. “It’s the guy from the ad!” Everyone within range turned in the direction of his avatar.

“No it isn’t,” a visitor objected.

“Yes. That’s the dude who fell. Hey, Lance!” they shouted at another visitor who’d been trying climb a wall. Lance paused to look at Mario.

“Isn’t that the guy from the Waterfall ad?”

Mario was speechless as word of him spread exponentially from visitor to visitor like some kind of virus. Nevertheless, a clique of regulars cast their doubts:

“He’s not that good.”

Mario glanced up. The regulars were sitting in their previous spot on the ledge of the third level.

“He fell, remember?”

Someone booed and Mario felt the blood rushing to his face. Suddenly it hit him: he could do it again. He could complete his run to the top of the cubes.

He changed outfits, control scheme, and sucked in air from muscle memory.

“He’s gonna run!” Someone yelled from under the small bridge. “Get out of the way!”

Just like before, Mario ran towards the wall and jump-kicked to the bridge. Then he sprinted, leapt, flipped and climbed his way to the top ledge.

“Whoa,” the two regulars stood up and made room for him.

“How’d you do it?” One of them demanded.

“Cheater,” came an accusation. “He hacked his controller.”

But the climb had been challenging and he struggled to focus. Balance, he thought.

This ledge is mine.

________

Mario stood. So long as he didn’t move, the water current inched him towards the fall.

Balance. He concentrated while eyeing the graffiti-tagged column. Then, he sprang towards it and climbed compulsively. The crowd looked on and, from ground level, Cherry saw her friend climbing higher and higher.

“Yeah!” She shouted as Mario reached the top of the cubes and...

Vanished.

________

“What?!” Bryce yelled into an empty apartment. He’d crashed back to the VR dashboard, his GPU running hotter than a nuclear summer.

It took a minute or so for him to reorient himself with being back in the real world. He removed the head-mounted display, unpaired the brain input controller, and checked the time.

It was 3 o’clock in the morning.

A ringtone sounded. It was Alexia.

“Bryce? What happened?”

“I’m having some technical issues.” Bryce put on a pair of smart glasses, which settled comfortably in the small groove in the bridge of his nose, made by the display after hours of wear.

“They’re saying you were kicked for using a recorder”.

Bryce removed the glasses, rubbed his eyes, replaced the glasses and peered through a window. City lights strobed as his pupils adjusted to reality’s infinite depth.

“Staring at the city?” she guessed after sending him a message. “Looks like you’re about to crash in real-time.”

“Yeah,” he resigned. And with that he disconnected the call.

After commanding Google Home to shut off the lights, Bryce checked Alexia’s message. It was an invitation to M.C. Escher’s Relativity.

He laughed, saved the invitation, and hand-rolled his wheelchair to bed.

______

Hexel art by Andrew Hicks

[notreallyherehahaha]

Chiral Symmetrohedron #2

In the last post here, I displayed a chiral symmetrohedron derived from the snub dodecahedron, and today I am presenting its “little brother,” which is derived from the snub cube. Both models were created using the “morph duals by truncation” function of Stella 4d: Polyhedron Navigator, a program you can download and try, for free, at this website. This newer solid contains six squares, 32…

[fromthedust]

A.L. Moure Strangis (Argentine, b.1956)

Monumento piramidal (Pyramid monument) four views - cement and plaster - 2015

El horno de los condenados (The oven of the damned) four views - cement - 2015

Portal tórico - Espacio místico para la contemplación (Toric portal - Mystical space for contemplation) four views - tinted cement - 2016

Monumento troncopiramidal - piramide roja (Truncated pyramid monument - red pyramid) ten views - tinted cement - 2015

Templo en el huevo (Temple in the egg) five views - cement - 2015

Esfera dentro de un cubo -  Espacio consagrado a la mística y la meditación (Sphere within a cube - Space dedicated to mysticism and meditation) four views - tinted cement - 2015  

https://almstrangis.tumblr.com/

[madeofkaons]

a lot of geometry-interested people know about truncation (and for good reason, seeing as it gives us a lot of the Archimedean solids from the Platonic solids), but I think more of us should talk about geometrical chamfering, also known as edge-truncation. this operation is essentially truncating the edges of a polyhedron instead of the vertices! chamfering a cube results in the chamfered cube, which is a near-miss Johnson solid. you can also think of chamfering as adding hexagonal faces where each edge of a shape originally was. repeatedly chamfering a shape gives you a sequence of Goldberg polyhedra, which is really neat.

above, from left to right: the chamfered icosahedron, chamfered dodecahedron, and chamfered cube.

image sources: T. Piesk, Polyhedron chamfered 20 edeq max, 11 February 2018, https://en.wikipedia.org/wiki/Chamfer_(geometry), CC BY 4.0. T. Piesk, Polyhedron chamfered 12 edeq max, 11 February 2018, https://en.wikipedia.org/wiki/Chamfer_(geometry), CC BY 4.0. T. Piesk, Polyhedron chamfered 6 edeq max.png, 11 February 2018, https://en.wikipedia.org/wiki/Chamfer_(geometry), CC BY 4.0.

[knotty-et-al]

Polyhedra on dotted isometric paper

Drawing polyhedra on dotted isometric paper is so calming. One does not need to use a ruler or a compass. Instead one can just count dots to determine the length, and play around with the angles.

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 3

Propaganda

Cube:

Also called the Regular Hexahedron

Platonic Solid

Regular

Dual of the Regular Octahedron

It has 6 square faces, 12 edges, and 8 vertices.

Oh, cmon! The cube is great! It tiles space, its one of the platonic solids that has analouges in all dimensionalities, its vertices are can be mapped to the strings of three binary digits in a structurepreserving way, and its literally the most iconic shape of all time!

Image Credit: Tumblr

Rhombicuboctahedron:

Also called the Small Rhombicuboctahedron

Archimedean Solid

Semiregular

Dual of the Deltoidal Icositetrahedron

It has 18 square faces, 8 regular triangular faces, 48 edges, and 24 vertices.

Image Credit: @anonymous-leemur

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

Image Credit: @anonymous-leemur

[art-of-mathematics]

Drawing a snub dodecahedron (in isometric perspective) is quite lot of work, because I have to start with a dodecahedron (easy), then make an isocidodecahedron out of it (quite a lot of work) , and then make a truncated icosidodecahedron out of it (very much work) and then, after all these steps I can make the snub dodecahedron from this.

It is a similar procedure I used for drawing the snub cube:

Started with cube, then cuboctahedron, then truncated cuboctahedron, then snub cube.

[kaishirase]

This model was designed by Alex Doskey using Great Stella. It was then exported to VRML format, which was used to build the physical model in a ZCorp stereolithograph machine. The model is only about 6 inches across, and has all regular non-intersecting faces.

Models by Adam Stolicki

Models by Adam Stolicki

Model by Adam Stolicki Model by Adam Stolicki Models by Adam Stolicki

Model by Adam Stolicki Model by Adam Stolicki Models by Adam Stolicki

Models by Giacomo Artoni

Hollow spherical model Stellation of Small Icosihemidodecahedron Stellation of Snub Cube Stellation of Great Dodecahemidodecahedron

Hollow spherical model

designed using this tutorial Compound of 6 Dodecahedra Stellation of Small Stellated

Truncated Dodecahedron Compound of 5 Octahedra

Models by Richard Stratton

Stellation of Great Ditrigonal Dodecicosidodecahedron Stellation of Small Icosihemidodecahedron Stellation of Snub Cube Stellation of Great Dodecahemidodecahedron

Stellation of Great Ditrigonal

Dodecicosidodecahedron Stellation of Small

Icosihemidodecahedron Stellation of Snub Cube Stellation of Great

Dodecahemidodecahedron

Models by Marc Picquendar

Stellation of Rhombic Triacontahedron Stellation of Rhombic Triacontahedron Small Snub Icosicosidodecahedron

Stellation of Rhombic Triacontahedron Final Stellation of Rhombic

Triacontahedron Small Snub

Icosicosidodecahedron

Compound of 5 Cubes Stellation of Truncated Octahedron Pentagonal Hexecontahedron Pentagonal Icositetrahedron

Compound of 5 Cubes Stellation of Truncated

Octahedron Pentagonal

Hexecontahedron Pentagonal

Icositetrahedron

Models by Robert Rech

Stellation of Great Ditrigonal Dodecicosidodecahedron Stellation of Small Icosihemidodecahedron

Stellation of Strombic Icositetrahedron Stellation of Triakisoctahedron

Models by Linda Zurich

Stellation of Cubitruncated Cuboctahedron Another stellation Stellation of Icosahedron Another stellation

Stellation of Cubitruncated

Cuboctahedron Another stellation Stellation of Icosahedron Another stellation

Models by Karlos Alonso Mediavilla

Compound of 5 Tetrahedra Compound of 3 Cubes Faceted Cube Compound of Dodecahedron and Great Dodecahedron

Compound of 5 Tetrahedra Compound of 3 Cubes Faceted Cube Compound of Dodecahedron

and Great Dodecahedron

Models by Steve Waterman

Waterman polyhedra

The first ten Waterman polyhedra in each of the three types available in Great Stella.

Models by Michael Barltrop

Compound of 15 Cuboids Compound of 4 Cubes Stellation of the Small Dodecahemicosahedron

Compound of 15 Cuboids Compound of 4 Cubes Stellation of the Small Dodecahemicosahedron

Monoacral stellation of Compound of 15 Cuboids Stellation of Small Dodecahemicosahedron Stellation of Great Dodecahemicosahedron

Monoacral stellation of

Compound of 15 Cuboids Stellation of Small Dodecahemicosahedron Stellation of Great Dodecahemicosahedron

A stellation Stellation of Small Stellated Truncated Dodecahedron

Stellation of the first Faceted

Rhombicosidodecahedron found in

Stella's Library Stellation of Small Stellated

Truncated Dodecahedron

Models by Keith Davison

See also: What people have to say about Stella.

[geommatrix]

Seni Lawal 324 mm  concrete Truncated cube

[educadacademy]

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Manage constraints

Create and maintain indexes including invisible indexes and multiple indexes on the same columns

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Controlling User Access

Differentiate system privileges from object privileges

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Manipulating Large Data Sets

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Describe the features of multitable INSERTs

Use multitable inserts

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Merge rows in a table

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from_tz

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to_timestamp_tz

to_yminterval

to_dsinterval

current_date

current_timestamp

localtimestamp

dbtimezone

sessiontimezone

Generating Reports by Grouping Related Data

Use the ROLLUP operation to produce subtotal values

Use the CUBE operation to produce crosstabulation values

Use the GROUPING function to identify the row values created by ROLLUP or CUBE

Use GROUPING SETS to produce a single result set

Retrieving Data Using Subqueries

Use multiple-column subqueries

Use scalar subqueries

Use correlated subqueries

Update and delete rows using correlated subqueries

Use the EXISTS and NOT EXISTS operators

Use the WITH clause

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Interpret the concept of a hierarchical query

Create a tree-structured report

Format hierarchical data

Exclude branches from the tree structure

Regular Expression Support

Use meta Characters

Use regular expression functions to search, match and replace

Use replacing patterns

Use regular expressions and check constraints

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