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
Faces38:
8 equilateral triangles
24 isosceles triangles
6 octagons
Edges72
Vertices12+24
Schläfli symbolrt{4,3}
Conway notationatC
Symmetry groupOh, [4,3], (*432), order 48
Rotation groupO, [4,3]+, (432), order 24
Dual polyhedronJoined truncated cube
Propertiesconvex
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.

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

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
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