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

Hemihypercube adjacency matrices

Finite affine plane of order 2, containing 4 points and 6 lines

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)