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

See also

• Rectified truncated tetrahedron
• 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-Strauss, 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