First Shape Found That Can't Pass Through Itself

Mathematicians have identified the first shape that cannot pass through itself. Jakob Steininger and Sergey Yurkevich described the Noperthedron in a paper posted online in August. The shape has 90 vertices and 152 faces. The discovery resolves a question that began in the late 1600s when Prince Rupert of the Rhine won a bet by proving one cube could slide through a tunnel bored through another. Mathematician John Wallis confirmed this mathematically in 1693.

The property became known as the Rupert property. In 1968, Christoph Scriba proved the tetrahedron and octahedron also possess this quality. Over the past decade, researchers found Rupert tunnels through many symmetric polyhedra, including the dodecahedron and icosahedron. Mathematicians had conjectured every convex polyhedron would have the Rupert property. Steininger and Yurkevich divided the space of possible orientations into approximately 18 million blocks and tested each. None produced a passage. The Noperthedron consists of 150 triangles and two regular 15-sided polygons.

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