Rectified truncated cube

Rectified truncated cube
Schläfli symbol	rt{4,3}
Conway notation	atC
Faces	38: 8 {3} 24 { }∨( ) 6 {8}
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 cube
Properties	convex
Net

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.

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-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