# Message #1470

From: Andrey <andreyastrelin@yahoo.com>

Subject: Re: Twists description

Date: Wed, 02 Mar 2011 05:51:57 -0000

Small correction to the "alternated" concept.

Flag "Alternated" is not common for the whole puzzle. It can be applied to any movement. If puzzle description contains one or more "alternated" mirror reflections, then valid movements are such that are compositions of an even number of alternated reflections and arbitary number of non-alternated reflections. This is important for the generation of axes set and for the generation of verteces as well.

Otherwise it will be difficult to describe something like "antiprismatic prisms".

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.

Andrey

— In 4D_Cubing@yahoogroups.com, "Andrey" <andreyastrelin@…> wrote:

>

> Re: Twists description

>

> http://groups.yahoo.com/group/4D_Cubing/photos/album/1184359940/pic/1892727590/view

>

> Description of 3D 4-antiprism:

>

> Dimensions: 3

> Movements: 0 0 1 ; 1 0 0 ; 2.4142135 1 0

> Vertices: 2.4142135 1 1

> Alternated: Yes

> Vector: 0 0 1

> Planes: 1 0 0 , 1 1 0

> Cuts: -0.4142135 ; 0.4142135

> Vector: 1 0 0

> Planes: 0 0 1 , 0 1 0

> Cuts: -1.4142135 ; 1.4142135

>