| Faces: | 38: 24 isosceles triangles 6 squares 8 hexagons |
| Edges: | 72 |
| Vertices: | 12+24 |
| Symmetry: | order 48 |
| Rotation Group: | order 24 |
| Dual: | Joined truncated octahedron |
| Properties: | convex |
| Net: | Rectified truncated octahedron net.png |
In geometry, the rectified truncated octahedron is a convex polyhedron, constructed as a rectified, truncated octahedron. It has 38 faces: 24 isosceles triangles, 6 squares, and 8 hexagons.
Topologically, the squares corresponding to the octahedron's vertices are always regular, although the hexagons, while having equal edge lengths, do not have the same edge lengths with the squares, having different but alternating angles, causing the triangles to be isosceles instead.
The rectified truncated octahedron can be seen in sequence of rectification and truncation operations from the octahedron. Further truncation, and alternation creates two more polyhedra: