Rectified truncated octahedron

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

Rectified truncated octahedron
Schläfli symbolrt{3,4}
Conway notationatO
Faces38:
24 { }∨()
6 {4}
8 {6}
Edges72
Vertices12+24
Symmetry groupOh, [4,3], (*432) order 48
Rotation groupO, [4,3]+, (432), order 24
Dual polyhedronJoined truncated octahedron
Propertiesconvex

Net

Topologically, the squares corresponding to the octahedron's vertices are always regular, although the hexagons, while having equal edge lengths, do not have the same edge lengths with the squares, having different but alternating angles, causing the triangles to be isosceles instead.

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

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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