Rectified truncated octahedron

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

The rectified truncated octahedron is a polyhedron, constructed as a rectified truncated octahedron. It has 38 faces: 24 isosceles triangles, 6 squares, and 8 regular hexagons.

Related polyhedra

The rectified truncated octahedron can be seen in sequence of rectification and truncation operations from the octahedron. Further truncation, and alternation creates two more polyhedra:

Name	Truncated octahedron	Rectified truncated octahedron	Truncated rectified truncated octahedron	Snub rectified truncated octahedron
Coxeter	tO	rtO	trtO	srtO
Conway		atO	btO	stO
Image
Conway	dtO = kC	jtO	mtO	mtO
Dual

See also

• Rectified truncated tetrahedron
• Rectified truncated cube
• 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