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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 They described the new shape May 28 in a paper published to the preprint database arXiv, though it has not yet been peer reviewed.related stories—Mathematicians make rare breakthrough on notoriously tricky ‘Ramsey problem’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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Love’s DQ gives Smith Xfinity win at Rockingham

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Love's DQ gives Smith Xfinity win at Rockingham

ROCKINGHAM, N.C. — JR Motorsports driver Sammy Smith was declared the winner of the NASCAR Xfinity Series race on Saturday at Rockingham Speedway.

Richard Childress Racing’s Jesse Love initially was announced as winning the race, but he was disqualified in postrace technical inspection for issues on the rear suspension and credited with a 37th-place finish.

Smith also picked up the final $100,000 Dash 4 Cash bonus prize of the year at the first Xfinity Series race at Rockingham Speedway in over two decades.

With Love’s disqualification, Alpha Prime Racing’s Parker Retzlaff was promoted to second place, a career best. Harrison Burton, Brennan Poole and Taylor Gray rounded out the top five.

Austin Hill, Josh Williams, Jeb Burton, Daniel Dye and Jeremy Clements completed the top 10.

Joe Gibbs Racing’s Justin Bonsignore also was disqualified from the race for three or more lug nuts not safe and secure, dropping the No. 19 Toyota from 36th place to 38th.

The red flag came out after a wreck on the restart with 10 laps remaining. With drivers close on fuel, Kaulig Racing’s Christian Eckes sputtered coming up to speed, causing a multicar incident that swept up Dash 4 Cash drivers Justin Allgaier and Brandon Jones. That led to another late-race stoppage.

Jones and Allgaier finished 12th and 21st, respectively. The final Dash 4 Cash competitor, Carson Kvapil, finished 16th.

Love led 53 laps and Ryan Sieg, who finished 18th, a race-best 77 laps.

The Xfinity Series returns to action next Saturday at Talladega (Ala.) Superspeedway for the Ag-Pro 300 (4 p.m. ET, The CW, MRN Radio, SiriusXM NASCAR Radio).

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Husband describes ‘horror’ as wife fatally hit by van at golf course after police chase

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Husband describes 'horror' as wife fatally hit by van at golf course after police chase

A husband has described how he watched in “helpless horror” as his wife was fatally hit by a van at a golf course after the vehicle was involved in a police chase.

Suzanne Cherry, 62, died in hospital four days after she was struck on the morning of 11 April, Staffordshire Police said.

Two patrol cars had been following the grey Nissan van in Kingstanding, Birmingham, after receiving reports of suspicious activity, according to the Independent Office for Police Conduct (IOPC).

They stopped chasing the van when it came off the road and went up an embankment at Aston Wood Golf Club, where it hit Ms Cherry, of Aldridge, Walsall.

In a statement released by police, Ms Cherry’s husband – who was not named – paid tribute to his “beautiful wife” and said her death leaves an “unfillable void” in the lives of her family.

“While enjoying what should have been the safest of one of Suzanne’s many activities, I watched in helpless horror as the life of my beautiful wife and our future together was snatched away in an instant,” he said.

Ms Cherry’s husband said she had “an amazing and infectious zest for life”, adding: “Suzanne leaves a legacy and an unfillable void in the lives of her mother Maureen, her three adult children, two step-children and countless others from her work, her sporting activities and social circle.

“Sue was loved, and will be painfully missed by her entire family and friends, we ask that our privacy at this difficult time be respected.”

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Officers from three different forces have arrested six men in connection with the incident.

The IOPC is continuing to investigate the circumstances before the collision.

Police are continuing to appeal for witnesses to come forward.

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Prince Andrew joins King and Queen at Easter Sunday church service

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Prince Andrew joins King and Queen at Easter Sunday church service

Prince Andrew was among members of the royal family who attended the traditional Easter Sunday service in Windsor.

It is the second year in a row that the Duke of York has joined the King and Queen at St George’s Chapel, appearing to enter the chapel quickly after his eldest brother’s arrival.

Other members of the royal family, including Princess Anne, the Duke and Duchess of Edinburgh, Princess Eugenie and Princess Beatrice and Andrew’s ex-wife Sarah Ferguson, also gathered outside the church.

The Duke of York leaves after attending the Easter Mattins service at St George's Chapel in Windsor Castle, Berkshire. Picture date: Sunday April 20, 2025.
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The Duke of York leaving St George’s Chapel. Pic: PA

William and Kate did not attend the annual service, deciding instead to spend time with their children, George, Charlotte and Louis, in Norfolk before they go back to school.

Crowds wished the King and Queen a Happy Easter as they left the chapel, with two children presenting Camilla with a bunch of flowers, before they were driven away.

King Charles III and Queen Camilla attend the Easter Mattins service at St George's Chapel in Windsor Castle, Berkshire. Picture date: Sunday April 20, 2025.
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King Charles and Queen Camilla arriving at St George’s chapel. Pic: PA

The Princess Royal speaks with the Dean of Windsor, the Right Rev Christopher Cocksworth, as she arrives for the Easter Mattins service at St George's Chapel in Windsor Castle, Berkshire. Picture date: Sunday April 20, 2025.
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The Princess Royal. Pic: PA

Andrew was seen glancing at a member of the crowd, who wished him a “Happy Easter” before the duke walked off with his ex-wife.

The duke has not been pictured at a formal royal family event since last Easter. He missed the royal family’s traditional Christmas gathering at Sandringham amid the controversy surrounding his links to an alleged Chinese spy.

He disappeared from public life after stepping down from official duties in March 2020, following his explosive TV interview with BBC’s Newsnight.

The Duchess of Edinburgh followed by Princess Eugenie and her husband Jack Brooksbank and Princess Beatrice arrive for the Easter Mattins service at St George's Chapel in Windsor Castle, Berkshire. Picture date: Sunday April 20, 2025.
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The Duchess of Edinburgh followed by Princess Eugenie and Princess Beatrice. Pic: PA

Sarah, Duchess of York, waves to the crowd as she attends the Easter Mattins service at St George's Chapel in Windsor Castle, Berkshire. Picture date: Sunday April 20, 2025.
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Sarah Ferguson. Pic: PA

The Easter sermon is traditionally led by the Archbishop of Canterbury, but was today led by the Archbishop of York, Stephen Cottrell, from York Minster.

Mr Cottrell has temporarily taken over the role after Justin Welby announced he was stepping down in November last year, after an independent review found he “could and should” have reported decades-long abuse of men and young boys by his former friend, the barrister John Smyth QC.

Mr Cottrell has also apologised for his handling of the case.

King Charles III and Queen Camilla leave after attending the Easter Mattins service at St George's Chapel in Windsor Castle, Berkshire. Picture date: Sunday April 20, 2025.
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Pic: PA

Queen Camilla waves to the crowd as she holds a posy after attending the Easter Mattins service at St George's Chapel in Windsor Castle, Berkshire. Picture date: Sunday April 20, 2025.
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The Queen waves to crowds in Windsor. Pic: PA

King’s message of ‘faith, hope and love’

Last year’s Easter Sunday service was the King’s first major public appearance after he announced his cancer diagnosis.

The 76-year-old monarch is still receiving treatment for cancer, and last month, spent a short period of time in hospital after experiencing temporary side effects.

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King and Queen attend Maundy service

In his Easter message – a tradition he started when he was the Prince of Wales – Charles reflected on the examples of “great cruelty and great kindness” that “daily come before our eyes” – saying they should remind the world of the importance of the “virtues of faith, hope and love”.

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He shared the message last week ahead of attending the annual Maundy service at Durham Cathedral, where he presented the Maundy recipients – 76 men and 76 women – with two purses: one red and one white, containing Maundy Money.

The ancient tradition traces back to the 13th century and is given to recipients in recognition of outstanding Christian service and work in their local communities.

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