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This Weird Pyramid Always Lands on the Same Face, Confirming 40-Year-Old Theory

“Bille” is the first-ever monostable tetrahedron, or a pyramid-like shape with four triangular faces that has one stable resting position. What this means is that Bille, no matter how you throw it and how it lands, will flip back on exactly the same side every single time. In a recent preprint submitted to arXiv, mathematicians revealed the first physical model of Bille, closing a decades-old theory proposed by the renowned British mathematician John Conway. Made of lightweight carbon fiber and

A new pyramid-like shape always lands the same side up

In 360 BCE, Plato envisioned the cosmos as an arrangement of five geometric shapes: flat-sided solids called polyhedra. These immediately became important objects of mathematical study. So it might be surprising that, millennia later, mysteries still surround even the simplest shape in Plato’s polyhedral universe: the tetrahedron, which has just four triangular faces. One major open problem, for instance, asks how densely you can pack “regular” tetrahedra, which have identical faces. Another as

A New Pyramid-Like Shape Always Lands the Same Side Up

In 360 BCE, Plato envisioned the cosmos as an arrangement of five geometric shapes: flat-sided solids called polyhedra. These immediately became important objects of mathematical study. So it might be surprising that, millennia later, mysteries still surround even the simplest shape in Plato’s polyhedral universe: the tetrahedron, which has just four triangular faces. One major open problem, for instance, asks how densely you can pack “regular” tetrahedra, which have identical faces. Another as