Triakis octahedron

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Triakis octahedron
(Click here for rotating model)
Type	Catalan solid
Face type	isosceles triangle
Faces	24
Edges	36
Vertices	14
Vertices by type	8{3}+6{8}
Face configuration	V3.8.8
Symmetry group	O_h
Dihedral angle	147°21'0"
Dual	Truncated cube
Properties	convex, face-transitive
Net

A triakis octahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated cube.

It can be seen as an octahedron with triangular pyramids added to each face, and is also sometimes called a trisoctahedron, or, more fully, trigonal trisoctahedron. Both names reflect the fact that it has three triangular faces for every face of an octahedron. The tetragonal trisoctahedron is another name for the deltoidal icositetrahedron, a different polyhedron with three quadrilateral faces for every face of an octahedron.

This convex polyhedron is topologically similar to the concave stellated octahedron. They have the same face connectivity, but the vertices are in different relative distances from the center.

[edit] Cultural references

A triakis octahedron is a vital element in the plot of cult author Hugh Cook's novel The Wishstone and the Wonderworkers.

[edit] References

Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)