Given I have enough trouble with tetraspace, this may be a silly question:
In 5d, the demipenteract appears to have an unknown dual (according to Wikipedia). If there were none, I'd assume this to be stated.
So I had a look and it appears this is the case for all demihypercubes for 5d and over.
In 4d, it's interesting that the demitesseract is the directly analogous to the orthoplex / 16-cell. Therefore the tesseract appears to be dual of its own 'half'
As this doesn't appear to be the case in 5d, can we start at a hypothesis that a demipentacross must exist as the dual of the demipenteract? Can a demipentacross exist, or is there some hypertopological constraint (dihedral angle?) that makes such a figure impossible?