## New Uniform Polytera+Symmetries

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

### New Uniform Polytera+Symmetries

I recently discovered many new uniform polytera.

The rat regiment contains a compound of 10 squocts, bic. Now consider the planes that the square bases of each squoct lie on. Each one contains 2 of penteractic symmetry’s 5 tesseractic axes. If we represent each axis with a vertex and connect them with an edge if a square base of a squoct uses both of them, we get a pentachoron graph. Removing half the squocts so that the graph becomes that of a pentagon results in a uniform compound of 5 squocts. This compound can blend with any rat troop that has either opes or tisdips, giving rise to 14 new uniforms. This same construction can also be applied to other compounds of 5 polytopes with the same symmetry as squoct that can be inscribed in a pentic uniform, which should lead to many more uniform polytera.
Mecejide
Trionian

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### Re: New Uniform Polytera+Symmetries

If I am understanding this correctly, what you have found is something like the 100+ new troops of the Hax regiment in 6D, but in 5D with the Rat regiment?
_Geometer
Mononian

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### Re: New Uniform Polytera+Symmetries

Yes. And not just 5D; all dimensions of the form https://oeis.org/A002144, at the very least.
Mecejide
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### Re: New Uniform Polytera+Symmetries

I wonder if there could be a uniform in the rat regiment with thahp terons?
ndl
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