Hemipolytope

Hemipolytopes are polytopes with facets that pass through the center of the polytope. They are often derived as facetings of other polytopes. All polytopes in the demicross series are uniform hemipolytopes, but not all hemipolytopes are demicrosses.

The facets which pass through the center are the hemi facets.

While there are no uniform hemipolygons, the infinite series of centered polypods are semi-uniform. The bowtie, a faceted rectangle, is a similar case outside of this infinite family.

List of Uniform Hemipolyhedra
There are 10 uniform polyhedra which are hemipolyhedra.

Other Hemipolytopes
As previously mentioned, all polytopes in the demicross series are hemipolytopes. Likewise, a prism of a hemipolytope will result in another hemipolytope. A hemipolytope pyramid or tegum will result in another hemipolytope if the center of the original polytope's facets are the center of the polytope. Some of these hemipolytopes may not be considered hemipolytopes at all because they are trivial or uninteresting, such as the dyad.

Here is an incomplete list of hemipolytopes.