Steffen's polyhedron
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| Steffen's polyhedron | |
|---|---|
| Rank | 3 |
| Elements | |
| Faces | 2+2+2 isosceles triangles, 4+4 scalene triangles |
| Edges | 21 |
| Vertices | 9 |
| Abstract & topological properties | |
| Euler characteristic | 2 |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Convex | No |
Steffen's polyhedron (or Steffen's flexible polyhedron) is a flexible polyhedron with 14 triangular faces.[1] Discovered by Klaus Steffen in an unpublished paper, it was proven in 1997 to be the simplest flexible polyhedron with only triangular faces.
The edge lengths of Steffen's polyhedron can vary, creating polyhedra with varying flexibility. Lijingjiao et al. used multi-objective optimization to find a balance between maximizing the polyhedron's range of motion while keeping the edge lengths closest to equilateral.[2]
References[edit | edit source]
- ↑ McClure, Mark. "Steffen's flexible polyhedron."
- ↑ Lijingjiao et al. "Optimizing the Steffen flexible polyhedron."