Rectified truncated cube
In geometry, the rectified truncated cube is a polyhedron, constructed as a rectified, truncated cube. It has 38 faces: 8 equilateral triangles, 24 isosceles triangles, and 6 octagons.
| Rectified truncated cube | |
|---|---|
 | |
| Faces | 38: 8 equilateral triangles 24 isosceles triangles 6 octagons |
| Edges | 72 |
| Vertices | 12+24 |
| Schläfli symbol | rt{4,3} |
| Conway notation | atC |
| Symmetry group | Oh, [4,3], (*432), order 48 |
| Rotation group | O, [4,3]+, (432), order 24 |
| Dual polyhedron | Joined truncated cube |
| Properties | convex |
| Net | |
 | |
Topologically, the triangles corresponding to the cube's vertices are always equilateral, although the octagons, while having equal edge lengths, do not have the same edge lengths with the equilateral triangles, having different but alternating angles, causing the other triangles to be isosceles instead.
Related polyhedra
The rectified truncated cube can be seen in sequence of rectification and truncation operations from the cube. Further truncation, and alternation operations creates two more polyhedra:
| Name | Truncated cube |
Rectified truncated cube |
Truncated rectified truncated cube |
Snub rectified truncated cube |
|---|---|---|---|---|
| Coxeter | tC | rtC | trtC | srtC |
| Conway | atC | btC | stC | |
| Image |  |
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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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