Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.


Postby wendy » Wed Feb 10, 2016 11:28 am

This is a fairly mundane packing of spheres, at the vertices of three A5 tilings. It is part of the magic to link some A5 to some D5.

It corresponds to the vertices of the compound xoo3ooo3oxo3ooo3oox3ooo3z (where z is in RK notation *a) . Most of these figures are compounds, and thus don't have a # anything.

I calculated the volume of the reference voronii cell (such as would take a sphere of diam sqrt(2)), to be 2¼. This makes it the second most efficient packing of spheres in five dimensions. The record is held by D5 or E5, at 2. A5 itself comes in at 2.449 = sqrt(6). I've drawn a number of sketches of it, but it leaves me none the wiser. In particular, one of the deep holes is o3o3m3o3o, a figure bounded by twenty bi-triangular tegum (it is after all the bi-surtegmic hexateron.) This consists of an interesting set of edges of length q and h, being the hull over two invertex hexatera ho3oo3oo3oo3oh, or by student91's notation ho3oo3oo3oo3oh&#z.

It's hoped to find 12 deep holes in it, so that one can directly find the Coxeter-Todd lattice in 12 dimensions, of packing 2.037037 q,
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