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What has 14 sides, is full of curves, and can perfectly cover a surface with no gaps or overlaps? It’s not a riddle — it’s a “vampire einstein.”

In March, a retired printing technician named David Smith stumbled upon a remarkable discovery in the world of mathematics. He found a 13-sided shape that could completely tile a surface without ever repeating. The shape, nicknamed “the hat” for its vaguely fedora-like shape was the culmination of decades of hunting by mathematicians around the world.

Since 1961 mathematicians had wondered if such a shape could exist. At first, mathematicians found a set of 20,426 shapes that could tile together while creating a pattern that never repeats (in contrast to the tiles on a kitchen floor, which do create a repeating pattern). Eventually, mathematicians found a  set of 104 shapes that could create such a never-repeating tiling. 

The middle and right shapes are examples of ‘Spectres’ — 14-sided shapes that can be tiled infinitely without ever creating a repeating pattern. (Image credit: Smith et al.)

Then in the 1970’s physicist and Nobel prize winner Roger Penrose found a pair of shapes that together created anon-repeating tiling. And for decades since, mathematicians continued to wonder if the same trick could be done with only a single shape. That semi-mythical shape, known formally as an aperiodic monotile, came to be known as “the einstein,” which means “one stone” in German. 

But for all the celebration around Smith’s discovery of an einstein tile, there was one small fly in the ointment. In order to create the non-repeating tiling, the “hat” had to work with its mirror image. Technically it’s the same shape, just flipped, but some argued that Smith hadn’t really found a true einstein.

Now, however, Smith and his colleagues have laid those objections to rest: they’ve found a shape that can tile a surface without repeating or being flipped. They described the new shape May 28 in a paper published to the preprint database arXiv, though it has not yet been peer reviewed.related stories—Mathematicians make rare breakthrough on notoriously tricky ‘Ramsey problem’

—Centuries old ‘impossible math problem cracked using physics of Schrödinger’s cat

—Two mathematicians just solved a decades-old math riddle — and possibly the meaning of life

The team named their shape the “Spectre,” an homage to vampires that can’t see their own reflections and thus don’t need a mirror. 

“In plane tiling, it is completely standard that tiles may be reflected; nevertheless, some people were dissatisfied that the aperiodic hat monotile requires reflections to tile the plane,” co-author Joseph Samuel Meyers wrote on Mastodon. “In our new preprint, we present the Spectre, the first example of a vampire einstein: an aperiodic monotile that tiles the plane without reflections.”

To find the ghostly shape, the team started with the original “hat” shape and added an extra side to it. That new shape still required its mirror image to fully tile, but the researchers discovered that by transforming the 14-sided shape’s straight edges into curved ones, they could dispense with mirror images and work with just the one shape.

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‘We’re a very dangerous team now’: What all this winning means for the Red Sox’s trade deadline plans

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'We're a very dangerous team now': What all this winning means for the Red Sox's trade deadline plans

Just over a month ago, the Boston Red Sox traded Rafael Devers to the San Francisco Giants in a blockbuster deal that sent shockwaves through the industry. At the time of the trade, the Red Sox were just a game over .500. They went 3-7 in their first 10 games without Devers and looked to be fading out of contention.

As the team fell in the standings, rumors began to circulate that the slugging designated hitter wouldn’t be the only star traded out of Boston. But a 10-game win streak before the All-Star break has vaulted the Red Sox into the thick of the playoff race and provided some clarity about their trade deadline plans.

“Throughout the whole year, we thought we had a really good team,” assistant GM Paul Toboni told ESPN over the weekend. “We were kind of waiting for it to click. That streak reconfirmed the thought that we had a good team.”

Boston doesn’t have a lot of expiring contracts, so even without the win streak, a complete teardown was unlikely. Still, trading some of its outfield depth was a possibility. The Red Sox rank in the top 10 in OPS in right field, center field and left field thanks to Jarren Duran, Roman Anthony, Ceddanne Rafaela and Wilyer Abreu.

With that group helping the Red Sox hold an American League wild-card spot, the front office is likely to add pitching, according to sources familiar with their situation, while retaining the abundance of outfielders unless the club is blown away with an offer in the next 10 days.

“Having a surplus of good players isn’t a bad thing,” Toboni said. “The high-end depth is a really good thing. It’s not like we’re anxious to move away from that.”

With their outfield situation likely to be addressed in the offseason, the Red Sox have winning on their minds. A young core, highlighted by the arrival of Anthony and infielder Marcelo Mayer, has had some time to adjust to the majors, leaving the team’s veterans excited about the coming months.

“These guys have been here for a few months now,” Red Sox third baseman Alex Bregman said. “We’re starting to learn who we are as a group. The adjustments are being made quicker at this time of the year. It didn’t start out that way, but guys are wanting to learn and get better. You can see that in our growth this year.”

Bregman watched closely while he was out of the lineup because of a quad injury he sustained at the end of May. He has seen what winning baseball looks like during his time in Houston. It has taken the young Red Sox some time to get there.

“We’re a very dangerous team now, especially when we’re prepared and executing,” Bregman said. “We’ve played good for a while now.

“People will say this is a hot streak, but I believe this is who we are.”

As the calendar inches toward August, that’s the sentiment throughout the clubhouse, where the veterans who have been through the uncertainty of trade season are relieved to spend the next two weeks without trade chatter.

“The run we went on before the All-Star break, it was good. We needed something like that to get us back in the mix, restore some confidence,” starting pitcher Lucas Giolito said. “Right now, staying in the present is important, but I don’t think we have guys in this room too worried they’re going to get dealt or anything anymore.”

Two players who were brought in over the offseason might be the most relieved.

All-Star closer Aroldis Chapman, who has a 1.18 ERA and 17 saves, could have been one of Boston’s most sought-after deadline trade candidates had the front office elected to deal him.

When asked about possibly being moved, the 37-year-old, who is playing for his seventh major league club, smiled as he responded through his interpreter: “The team is in good shape.”

Fellow Boston pitcher Walker Buehler added: “It’s probably good timing to hopefully push the front office to go out and buy and help us make a run. We did our part at the end of the first half there. I want to stay here and be part of it. Don’t want to be on the wrong side of a trade.”

Though they might have done enough to convince the front office to stick with the current veterans, the Red Sox have some of their toughest work ahead of them. According to ESPN Research, they have the hardest remaining schedule for the rest of the month and sixth hardest for the rest of the season, but manager Alex Cora isn’t interested in looking at the stretch run — or what Boston’s first postseason berth since 2021 would mean.

Instead, he believes that if the players can keep attacking each day, the rest will take care of itself.

“I promised myself I’m going to stay in the moment,” Cora said. “It doesn’t do the group any good to start talking about that. We have to win games. It’s not to put pressure on the front office or ownership. It’s what we need to do for us to play in October.”

Opposing teams are asking for “outrageous returns” for pitching, according to league sources, but if the asking prices become more reasonable closer to the deadline, expect the Red Sox to be involved. Until then, they are focused on riding their July momentum while navigating a tough schedule.

“Time to keep it locked in,” Giolito said. “We’ll be welcoming whatever help comes.”

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Aventon Sinch 2 folding e-bike at $1,399 low, Autel AC Lite 50A level 2 EV charger $455, NIU KQi 300X e-scooter $750, EcoFlow, more

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Aventon Sinch 2 folding e-bike at ,399 low, Autel AC Lite 50A level 2 EV charger 5, NIU KQi 300X e-scooter 0, EcoFlow, more

Today’s Green Deals are all about EVs and power stations, with our headliner being Aventon’s Sinch 2 Folding e-bike at its $1,399 low. Right behind it, we have Autel’s MaxiCharger AC Lite Home Level 2 EV charger down at $455, as well as NIU’s KQi 300X All-Terrain Suspension Electric Scooter for $750. From there we have four limited-time EcoFlow member-only solar generator bundle deals at up to 56% off, Anker’s SOLIX C1000 power station, and a one-day-only sale on Anker’s SOLIX BP1000X expansion battery for the previously mentioned station. All these and more are waiting for you below. Plus, there’s all the hangover savings at the bottom of the page, like yesterday’s Anker PowerCore Reserve dropping under $90, Schumacher’s new portable level 1 EV charger, and more.

Head below for other New Green Deals we’ve found today and, of course, Electrek’s best EV buying and leasing deals. Also, check out the new Electrek Tesla Shop for the best deals on Tesla accessories.

Aventon’s space-saving Sinch 2 folding e-bike brings utility to your commutes for up to 55 miles at its $1,399 low

Among the selection of Aventon e-bikes retaining their post-July 4th Sale lows, we wanted to shine a spotlight on the brand’s Sinch 2 Folding e-bike that is still down at $1,399 shipped. Normally going for $1,699 at full price, we’ve mostly seen this model discounted to $1,499 over the last year, with more recent sales dropping the costs to its $1,399 low, mostly in response to the launch of the upgraded Sinch 2.5 descendant model. You’ll be saving $300 off the going rate while the savings last, giving you a space-saving commuter at the best price we have tracked.

Aventon’s Sinch 2 e-bike is the second-generation legacy model among its folding series of commuters, with the frame providing more space-saving functionality when storing or transporting it. It comes equipped with a 500W rear-hub motor (peaking at 1,056W) alongside a 672Wh battery in order to reach top speeds of 20 MPH for up to 55 miles of travel while its four PAS levels are activated, which come supported by a torque sensor. Of course, you’ll gain added utility thanks to included features like the rear cargo rack, with others including the integrated front and rear lighting that sport turn signal functionality, an 8-speed derailleur, fenders to go over both 20 by 4-inch tires, an LCD smart “easy read” display, and more.

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You can check out the full lineup of Aventon’s current deals in our original coverage of these extended savings here, which include models like the Level 2 Commuter e-bike still down at its $1,399 annual low. You can also find the brand’s new Pace 4 Step-Through Cruiser e-bike that comes with an array of smart features still benefitting from its first-ever savings at $1,699 too.

man using Autel AC Lite 50A level 2 EV charger to charge EV

Install Autel’s MaxiCharger AC Lite level 2 EV charger at home for up to 50A speeds for $455

Through its official Amazon storefront, Autel is offering Prime members its MaxiCharger AC Lite Home Level 2 EV charger back at $455.20 shipped, which we’re also seeing matched in price direct from the brand’s website. While this model goes for $569 at full price directly from the manufacturer, we’ve regularly been seeing it keep down to this same rate for most of 2025, with things only falling lower in that period to $450 during Prime Day two weeks ago. You can take advantage of the 20% savings that cuts $114 off the tag for the third-lowest price we have tracked – $56 above the low from Black Friday.

If you want to learn more about this at-home EV charger, be sure to check out our original coverage of this deal here.

man posing on NIU KQi 300X electric scooter

NIU’s 37-mile trekking KQi 300X all-terrain e-scooter with hydraulic suspension and regen braking at $750

NIU’s official Amazon storefront is now offering its KQi 300X All-Terrain Suspension Electric Scooter for $749.99 shipped, which is also matching in price direct from NIU’s website. While this higher-end model from the brand would cost you $1,299 at full price, it keeps down between $1,049 and $1,198 at Amazon on average. From January to late June we mostly saw discounts taking things to $999, with more recent price cuts seeing drops lower to $919 and $899. While the deal here lasts, you’re looking at a 42% markdown from its MSRP, with up to $549 in savings landing it at the best price we’ve tracked in 2025, only beaten out by the $731 low we last saw in October 2024.

If you want to learn more about this NIU e-scooter, be sure to check out our original coverage of this deal here.

EcoFlow DELTA Pro power station sitting next tow extra battery and solar panel in yard

Score up to 56% savings on four EcoFlow bundles like the DELTA Pro with a 400W panel at $2,169

As part of EcoFlow’s current post-Prime Day power deals, the brand is offering up to 56% off four members-only bundle units through July 24, with sign-up being free, though we’re also seeing these or lower prices at Amazon for Prime members. Among the offers, a notable standout is the DELTA Pro Solar Generator bundle with a 400W panel that is down at $2,169 shipped, and also matching in price at Amazon. This package would normally run you $4,898 from the brand at full price, while we see it keep down at $3,999 at Amazon on average. This opportunity also beats out the costs of two of the current flash sale offers that give you the station, panel, and protective bag for $2,428 (though you won’t get the bag that adds $99 to that price). You’re looking at a 56% markdown with this bundle deal, saving you up to $2,729 at the second-lowest price we have tracked.

If you want to learn more about this solar generator package, as well as the other bundle deals, be sure to check out our original coverage here.

man powering griddle with Anker SOLIX c1000 power station

Cover power needs on camping trips through Anker’s SOLIX C1000 station at $469

By way of its official Amazon storefront, Anker is offering its SOLIX C1000 Portable Power Station at $469 shipped, beating out the brand’s direct pricing by $50. While this model fetches $999 at full price directly from the brand, we see it keep down at $799 when at full price at Amazon, with discounts having taken things as low as $429 in the past, which was last seen two weeks ago during the Prime Day event. If you missed out on the pricing then, you’re still looking at a solid 41% markdown off the going rate here (53% off its MSRP), giving you up to $530 savings at the third-lowest price we have tracked.

If you want to learn more about this model, be sure to check out our original coverage of this deal here.

man and woman having picnic on beach with Anker SOLIX C1000 power station and expansion battery

Expand your Anker SOLIX C1000 station with the BP1000 add-on battery at a new $380 low for today only

As part of its Deals of the Day, Best Buy is giving folks a small window to expand their Anker SOLIX C1000 setup with the BP1000X Expansion Battery at $379.99 shipped, which beats out Amazon’s pricing of the standard model by $49 and Anker’s direct pricing by $419. You’d normally have to shell out $799 for this add-on gear at full price, which we’ve seen discounted as low as $400, the most recent of which was back at the tail-end of March. All the deals we’ve ever seen before are getting beaten out here for the rest of the day, with the 52% markdown saving you $419 at the best new price we have tracked.

If you want to learn more about this expansion battery, be sure to check out our original coverage of this one-day-only sale here.

Best Summer EV deals!

Best new Green Deals landing this week

The savings this week are also continuing to a collection of other markdowns. To the same tune as the offers above, these all help you take a more energy-conscious approach to your routine. Winter means you can lock in even better off-season price cuts on electric tools for the lawn while saving on EVs and tons of other gear.

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The Hyundai IONIQ 2 is an affordable little brother to the IONIQ 5 [images]

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The Hyundai IONIQ 2 is an affordable little brother to the IONIQ 5 [images]

The Hyundai IONIQ 2 was just spotted out in public for the first time. Hyundai is expected to introduce the smaller, more affordable EV later this year. Here’s our first look at the IONIQ 5’s little brother.

The Hyundai IONIQ 2 is coming in just a few months

According to Xavier Martinet, president and CEO of Hyundai’s European operations, the new EV will debut “in the next few months.”

Hyundai is expected to showcase the electric crossover SUV at the Munich Motor Show in September. It will be underpinned by the same E-GMP platform that powers Hyundai’s other IONIQ models and the Kia EV lineup.

The new model is expected to arrive as the IONIQ 2, positioned between the Inster EV and Kona Electric in Hyundai’s electric vehicle lineup. Based on the same platform, Hyundai’s new EV will likely share components with the upcoming Kia EV2.

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Kia is launching the EV2, its smallest and most affordable EV, next year. The Hyundai IONIQ 2 is expected to arrive shortly after.

Ahead of its official debut, we are getting our first glimpse of Hyundai’s upcoming EV. A camouflaged prototype was spotted by Korean blogger ShortsCar in a parking garage.

Although it’s covered, the crossover SUV-like profile is still visible, similar to the EV2. You can also see Hyundai’s signature EV elements, such as pixelated lighting on the side mirrors and front LED headlights.

Like the EV3, it will likely be offered with several battery options, including a 58.3 kWh or 81.4 kWh battery pack. The standard range battery is rated for a WLTP range of 267 miles, while the extended range pack offers a range of up to 372 miles. Both variants are powered by a single front-mounted electric motor with 201 horsepower.

Hyundai-IONIQ-2
Kia Concept EV2 (Source: Kia)

Although it will share components with the EV2, the IONIQ 2, according to Autocar, will be a “step change” in terms of usability, featuring advanced new software and in-car features.

It will likely debut with Hyundai’s new Pleos software and infotainment system. The end-to-end software-defined platform connects everything from the vehicle’s infotainment to the operating system (OS) and then to the Cloud.

Hyundai-IONIQ-2-Pleos-infotainment
Hyundai’s next-gen infotainment system powered by Pleos (Source: Hyundai)

Hyundai plans to unlock new features, including self-driving capabilities and real-time data analysis. With an Android-based system, the infotainment system has a “smartphone-like UI,” offering new functions like multi-window viewing. It also comes with an AI voice assistant.

Hyundai-IONIQ-2
Kia EV3 Air in Frost Blue (Source: Kia UK)

Prices and final specs will be revealed closer to launch. However, given that the Kia EV3 starts at €35,990 ($42,500), the Hyundai IONIQ 2 is expected to start at around €30,000 ($35,400).

For those in the US, sorry to disappoint, but the IONIQ 2 is not likely to make the trip overseas. Hyundai is betting on bigger electric SUVs, including the IONIQ 5 and IONIQ 9.

The Kia EV3 is already the most popular retail EV in the UK. Will Hyundai’s IONIQ 2 see the same demand when it arrives?

Source: TheKoreanCarBlog, ShortsCar

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