# Triakis octahedron

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Triakis octahedron

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.

Cultural references

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

References

* (Section 3-9)

*
* [http://polyhedra.org/poly/show/34/triakis_octahedron Triakis Octahedron] -- Interactive Polyhedron Model
* [http://www.lifeisastoryproblem.org/explore/net_triakisoctahedron.pdf Printable Net of a Triakis Octahedron] [http://www.lifeisastoryproblem.org Life is a Story Problem.org]
* [http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] www.georgehart.com: The Encyclopedia of Polyhedra
** VRML [http://www.georgehart.com/virtual-polyhedra/vrml/triakisoctahedron.wrl model]
** [http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra] Try: "dtC"

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