Talk:Hemicube (geometry)

Better image
I strongly recommend using the image shown here instead: it provides the necessary information to work with this object. The maths has to be more important than the artistic qualities!


 * Looks good! Tom Ruen (talk) 04:36, 19 December 2008 (UTC)

Hyperhemicube


It seems to me, that each hyperhemicube is the hypercube of the lower dimension, with additional edges between all complements. Is that (at least topologically) correct?

Also: Isn't the hemicube quite the same as this affine plane from finite geometry? mate2code 17:12, 7 July 2013 (UTC)


 * Maybe? Ha! I don't have any sources or intuition to guess. I can see there's two different ways to consider extending to 4D. For one (which I assume is the correct way), you can compare to 2 abstract polytopes: 11-cell, {3,5,3} and 57-cell, {5,3,5}, made of abstract hemi-icosahedron and hemi-dodecahedron cells. So perhaps you can assemble hemicubes into a regular projective polytope? But apparently doesn't work?! Alternately you can take half of a tesseract with 4 cubic cells, but does it exist? Tom Ruen (talk) 23:56, 7 July 2013 (UTC)

Merge with cube?
Given the hemi-figures are all related to platonic solids, and short articles, perhaps they should be merged as sections the full/"spherical" ones? Tom Ruen (talk) 23:22, 6 January 2015 (UTC)