Jump to content

Rectified truncated octahedron

From Wikipedia, the free encyclopedia
Rectified truncated octahedron
Faces38:
24 isosceles triangles
6 squares
8 hexagons
Edges72
Vertices12+24
Schläfli symbolrt{3,4}
Conway notationatO
Symmetry groupOh, [4,3], (*432), order 48
Rotation groupO, [4,3]+, (432), order 24
Dual polyhedronJoined truncated octahedron
Propertiesconvex
Net

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

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.

[edit]

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

[edit]

References

[edit]
  • 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
[edit]