They started the mens match in style winning all six of the opening group and followed that up with another seven sets to win 13-3. Fife’s Colin Hepplewhite was their best on the day with a 78.82 average whilst Iain Campbell for Moray hit a 78.08. It’s not clear who first identified the Platonic solids. Perhaps it was the Pythagoreans (particularly living near so many polyhedrally shaped pyrite crystals). Perhaps it was someone long before them. Or perhaps it was a contemporary of Plato’s named Theaetetus. But in any case, by the time of Plato (≈400 BC), it was known that there are five Platonic solids. And when Euclid wrote his Elements (around 300 BC) perhaps the pinnacle of it was the proof that these five are all there can be. (This proof is notably the one that takes the most steps— 32—from the original axioms of the Elements.)

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Testing kits are available from the Advice Centre if you are worried that you have been a victim of spiking.The kits are effective up to 48 hours post-incident, but are not forensic and as such cannot be used to prove an incident occurred. Open conversation update Grampian also retained both the ladies and men’s leagues in the North with Fife second in both and Highland third in both. In the ladies match Courtney McBain from Highland took her third match award hitting a 54.00 average while Tay Valley’s Chel Rennie hit 47.21. League darts take a break this week as the A, B and C League singles are held in three venues across the city. Grampian have retained their title in the Darts Corner SDA Counties Championship as they finish top of the Accumulative Table in Scotland North on 87 points with Fife second on 72 and Highland third on 69.

Then he essentially considered pushing the centers of each face in or out to a specified multiple α of their usual distance from the center of the dodecahedron: For α< 1, the resulting faces don’t intersect. But for most values of α, they don’t have equal-length sides. That only happens for the specific case —and in that case the resulting polyhedron is exactly the rhombic hexecontahedron.

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Raging Storm Raigmore’s 8-4 win against Culloden Moor Inn enabled them to move into third spot in the table, a point ahead of Culloden but having played one more game. Over the next three centuries, more polyhedra, with various forms of regularity, were gradually found—and by the early 1900s there were many known to mathematicians: But ultimately I’m pretty sure that somewhere there’s a single origin for the folk Spikey. It’s not something that I suspect was invented more than once. By construction, these rhombuses (or, more strictly, shapes made from them) can’t form a repetitive pattern. But it turns out they can form a pattern that can be built up in a systematic, nested way:Both these winning sides will be defending their undefeated run in the league when they play each other on the 15 th June in Muir of Ord.

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Thousands of the free stoppers will now be delivered to pubs and bars across Sunderland after they received unanimous support from the city’s successful Pubwatch scheme. It's important to reiterate that the individuals are never at fault if they have been spiked, but it’s crucial that you’re aware of some preventative steps you can take to reduce the risk, what to do if you suspect an issue has happened, and ultimately how you can look out for yourself and your friends when you’re on a night out. Remember we’re not just talking about our venues here, this goes for anywhere you may be out drinking in the local community – including house parties. The symptoms will depend on lots of factors such as the substance or mix of substances used (including the dose), your size and weight, and how much alcohol you have already consumed. Needle spiking The top ladies set went to Joan Milne from Grampian with 53.49 whilst Angus player Helena Wild hit a 48.54 average. Seaforth Club made up some ground on the leaders with an 8-4 win over Still Game in Nairn and they inch up the table into fourth spot.

But, so far as I can tell, the rhombic hexecontahedron was not among them. And instead its discovery had to await the work of a certain Helmut Unkelbach. Born in 1910, he got a PhD in math at the University of Munich in 1937 (after initially studying physics). He wrote several papers about conformal mapping, and—perhaps through studying mappings of polyhedral domains—was led in 1940 to publish a paper (in German) about “The Edge-Symmetric Polyhedra”. By closing the gap between the straw and edge of the bottle you are greatly reducing the possibility of your drink being spiked. The City Taxis Inverness Summer Darts League approaches the half-way stage next week and things are very close in all three divisions. He was determined to keep darts going in the Highland area, spending a huge amount of his time arranging and running events and tournaments to keep the game alive. His records and archive contain a huge amount of information regarding darts across Scotland but filing was not his strong point. Drink spiking using (extra) alcohol, LSD, Rohypnol, or prescription drugs is a common and unfortunate criminal activity.

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Losing in the semi-finals were twice previous champion Jim MacNeil with Henry MacPherson from Innes Spikeys along with Barry Stuart and James McCabe, a previous champion in 2018.Then there are the 13 Archimedean solids, all of whose vertices are identical, and whose faces are regular polygons but of more than one kind: Letting people know gives the best chance of looking after you and gathering any evidence where a crime may have taken place. Report a crime Looking through my 1991 archives today, I find some “explanatory” code (by Ilan Vardi)—and it’s nice to see that it all just runs in our latest Wolfram Language (though now it can be written a bit more elegantly): There was another first-time champion in the B League competition at the Innes Bar as Raigmore’s Shaun Morrison defeated Dave King from Innes X, 3-1, in the final. Our Wolfram|Alpha Spikey burst onto the scene in 2009 with the release of Wolfram|Alpha. But we still had our long-running and progressively evolving Mathematica Spikey too. So when we built a new European headquarters in 2011 we had not just one, but two Spikeys vying to be on it.