{"id":16241,"date":"2025-08-11T16:35:52","date_gmt":"2025-08-11T16:35:52","guid":{"rendered":"https:\/\/topat10.com\/?p=16241"},"modified":"2025-08-11T16:35:52","modified_gmt":"2025-08-11T16:35:52","slug":"this-new-pyramid-like-shape-always-lands-with-the-same-side-up","status":"publish","type":"post","link":"https:\/\/topat10.com\/?p=16241","title":{"rendered":"This New Pyramid-Like Shape Always Lands With the Same Side Up"},"content":{"rendered":"


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In 2023, Domokos\u2014along with his graduate students Gerg\u0151 Alm\u00e1di and Krisztina Reg\u0151s, and Robert Dawson<\/a> of Saint Mary\u2019s University in Canada\u2014proved that it is indeed possible to distribute a tetrahedron\u2019s weight so that it will sit on just one face. At least in theory.<\/p>\n

But Alm\u00e1di, Dawson, and Domokos wanted to build the thing, a task that turned out to be far more challenging than they expected. Now, in a preprint posted online yesterday, they have presented the first working physical model<\/a> of the shape. The tetrahedron, which weighs 120 grams and measures 50 centimeters along its longest side, is made of lightweight carbon fiber and dense tungsten carbide. To work, it had to be engineered to a level of precision within one-tenth of a gram and one-tenth of a millimeter. But the final construction always flip-flops onto one face, exactly as it should.<\/p>\n

The work demonstrates the important role of experimentation and play in research mathematics. It also has potential practical applications, such as in the design of self-righting spacecraft.<\/p>\n

\u201cI didn\u2019t expect more work to come out on tetrahedra,\u201d Papp said. And yet, he added, the team\u2019s research allows mathematicians to \u201creally appreciate how much we didn\u2019t know and how thorough our understanding is now.\u201d<\/p>\n

Tipping Point<\/h2>\n

In 2022, Alm\u00e1di, then an undergraduate aspiring to become an architect, enrolled in Domokos\u2019 mechanics course. He didn\u2019t say much, but Domokos saw in him a hard worker who was constantly in deep thought. At the end of the semester, Domokos asked him to concoct a simple algorithm to explore how tetrahedra balance.<\/p>\n

When Conway originally posed his problem, his only option would have been to use pencil and paper to prove, through abstract mathematical reasoning, that monostable tetrahedra exist. It would have been almost prohibitively difficult to pinpoint a concrete example. But Alm\u00e1di, working decades later, had computers. He could do a brute-force search through a huge number of possible shapes. Eventually, Alm\u00e1di\u2019s program found the coordinates for the four vertices of a tetrahedron that, when assigned certain weight distributions, could be made monostable. Conway was right.<\/p>\n

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