geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, Steffen's polyhedron is a

flexible polyhedron In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes of all of its faces unchanged. The Cauchy rigidity theorem shows that in dimension 3 suc ...

discovered (in 1978) by and named after . It is based on the Bricard octahedron, but unlike the Bricard octahedron its surface does not cross itself.. With nine vertices, 21 edges, and 14 triangular faces, it is the simplest possible non-crossing flexible polyhedron. Its faces can be decomposed into three subsets: two six-triangle-patches from a Bricard octahedron, and two more triangles (the central two triangles of the net shown in the illustration) that link these patches together.. It obeys the

strong bellows conjecture In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes of all of its faces unchanged. The Cauchy rigidity theorem shows that in dimension 3 suc ...

, meaning that (like the Bricard octahedron on which it is based) its Dehn invariant stays constant as it flexes..

References

External links

Steffen's Polyhedron

Greg Egan Greg Egan (born 20 August 1961) is an Australian science fiction writer and amateur mathematician, best known for his works of hard science fiction. Egan has won multiple awards including the John W. Campbell Memorial Award, the Hugo Award, ...

Nonconvex polyhedra Mathematics of rigidity {{polyhedron-stub