Rectified truncated tetrahedron
| Rectified truncated tetrahedron | |
|---|---|
 | |
| Schläfli symbol | rt{3,3} |
| Conway notation | atT |
| Faces | 20: 4 {3} 12 { }∨( ) 4 {6} |
| Edges | 48 |
| Vertices | 12+18 |
| Symmetry group | Td, [3,3], (*332) order 24 |
| Rotation group | T, [3,3]+, (332), order 12 |
| Dual polyhedron | Joined truncated tetrahedron |
| Properties | convex |
 Net | |
The rectified truncated tetrahedron is a polyhedron, constructed as a rectified truncated tetrahedron. It has 20 faces: 4 equilateral triangles, 12 isosceles triangles, and 4 regular hexagons.
Related polyhedra
The rectified truncated tetrahedron can be seen in sequence of rectification and truncation operations from the tetrahedron. Further truncation, and alternation operations creates two more polyhedra:
| Name | Truncated tetrahedron |
Rectified truncated tetrahedron |
Truncated rectified truncated tetrahedron |
Snub rectified truncated tetrahedron |
|---|---|---|---|---|
| Coxeter | tT | rtT | trtT | srtT |
| Conway | atT | btT | stT | |
| Image |  |
|
 |
 |
| Conway | dtT = kT | jtT | mtT | gtT |
| Dual |  |
 |
 |
 |
See also
- Rectified truncated cube
- Rectified truncated octahedron
- 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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