Kleetope [SEP] named after
Kleetope
In geometry and polyhedral combinatorics, the Kleetope of a polyhedron or higher-dimensional convex polytope is another polyhedron or polytope formed by replacing each facet of with a shallow pyramid. Kleetopes are named after Victor Klee.
Examples.
The triakis tetrahedron is the Kleetope of a tetrahedron, the triakis octahedron is the Kleetope of an octahedron, and the triakis icosahedron is the Kleetope of an icosahedron. In each of these cases the Kleetope is formed by adding a triangular pyramid to each face of the original polyhedron. Conway
was given by to the networks they studied in which the level of subdivision of triangles is uniform across the network; these networks correspond geometrically to a type of stacked polyhedron called a Kleetope. Other authors applied the same name more broadly to planar 3-trees in their work generalizing the model of Andrade et al. to random Apollonian networks. The triangulations generated in this way have also been named "stacked triangulations" or "stack-triangulations".
See also.
- Barycentric subdivision, a different method of subdividing triangles into