Rectified truncated octahedron
| 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 | |
The rectified truncated octahedron is a polyhedron, constructed as a rectified truncated octahedron. It has 38 faces: 24 isosceles triangles, 6 squares, and 8 regular hexagons.
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 | gtO |
| Dual |  |
 |
 |
 |
See also
- Rectified truncated tetrahedron
- Rectified truncated cube
- Rectified truncated dodecahedron
- Rectified truncated icosahedron
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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