A polyhedron P has the Rupert property if a straight tunnel can be made in it, large enough so that a copy of P can pass through this tunnel. Eight Archimedean polyhedra are known to have the Ruper...

The Truncated Tetrahedron Is Rupert

It is a 300-year-old counterintuitive observation of Prince Rupert of the Rhine that in the cube a straight tunnel can be cut through which a second congruent cube can be passed. A hundred years la...

Cubes and Boxes Have Rupert’s Passages in Every Nontrivial Direction

A polyhedron is Rupert if it is possible to cut a hole in it and thread an identical polyhedron through the hole. It is known that all 5 Platonic solids, 10 of the 13 Archimedean solids, 9 of the 13 Catalan solids, and 82 of the 92 Johnson solids are Rupert. Here, a nonlinear optimization method is devised that is able to rediscover the previously known results in seconds. It is also used to show that 2 additional Catalan solids and 5 additional Johnson solids are Rupert.

The triakis tetrahedron and the pentagonal icositetrahedron are Rupert

An oval in is called Rupert if a straight tunnel can be made in it through which a second congruent oval can be passed. We show that the n-cube is Rupert for each n ⩾ 3.

Kay Pechenick Shultz

Papers

The n-Cube is Rupert