# Message #1471

From: Roice Nelson <roice3@gmail.com>

Subject: Re: [MC4D] Re: Twists description

Date: Wed, 02 Mar 2011 00:16:02 -0600

On Tue, Mar 1, 2011 at 11:51 PM, Andrey <andreyastrelin@yahoo.com> wrote:

>

> I still wonder why there are no alternated douprisms [2n]x[2k] in the list

> of uniform polychora. If we take checkerboard pattern on verteces of

> douprism and throw away all white verteces, what will be the convex hull of

> the remaining ones? Of cource, we must take different size of [2n] and [2k]

> polygons, length of their smallest diagonals should be the same.

I wouldn’t be able to prove it myself, but Wikipedia says the following on

the duoprism<http://en.wikipedia.org/wiki/Duoprism#Polychoral_duoantiprisms>

page…

Like the antiprisms as alternated prisms, there is a set of 4-dimensional

> duoantiprisms polychorons that can be created by an alternation operation

> applied to a duoprism. However most are not uniform. The alternated vertices

> create nonregular tetrahedral cells, except for the special case, the 4-4

> duoprism (tesseract) which creates the uniform (and regular) 16-cell. The

> 16-cell is the only convex uniform duoantiprism.

seeya,

Roice