Rectified truncated octahedron
The rectified truncated octahedron is a polyhedron, constructed as a rectified truncated octahedron. It has 38 faces: 24 isosceles triangles, 6 squares, and 8 hexagons.
| Rectified truncated octahedron | |
|---|---|
 | |
| Schläfli symbol | rt{3,4} |
| Conway notation | atO |
| Faces | 38: 24 { }∨() 6 {4} 8 {6} |
| Edges | 72 |
| Vertices | 12+24 |
| Symmetry group | Oh, [4,3], (*432) order 48 |
| Rotation group | O, [4,3]+, (432), order 24 |
| Dual polyhedron | Joined truncated octahedron |
| Properties | convex |
 Net | |
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.
Related polyhedra
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:
| Name | Truncated octahedron |
Rectified truncated octahedron |
Truncated rectified truncated octahedron |
Snub rectified truncated octahedron |
|---|---|---|---|---|
| Coxeter | tO | rtO | trtO | srtO |
| Conway | atO | btO | stO | |
| Image |  |
|
 |
 |
| Conway | dtO = kC | jtO | mtO | mtO |
| Dual |  |
 |
 |
 |
See also
References
- Coxeter Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8 (pp. 145–154 Chapter 8: Truncation)
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5
External links
- George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input
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