Skewing

Skewing, or skew halving, is an operation that can be performed on a regular polyhedron of Schläfli type. It is represented with the symbol.

It is equivalent to the composed operation &pi;&compfn;&delta;&compfn;&eta;&compfn;&pi;&compfn;&delta;, although in some cases the intermediate stages of this process may be degenerate or impossible to realize, while the end result is neither.

Abstract polytopes
The skewing of a regular polyhedron with distinguished generators $$\left(\rho_0,\rho_1,\rho_2\right)$$ is the regular polyhedron generated by the distinguished generators:

$$ \left(\rho_1, \rho_0\rho_2,(\rho_1\rho_2)^2\right) $$