apeirored.png copyright 08/18/2002 Wendy Krieger

This sequence shows development from the rr{;3,oo;}. The tyler setting here is 4,3,4,0.

The first is the rr{;3,oo;}. Like any rr{;3,p;}, the combination of the {p}-gon, and a layer of triangles and squares, gives a {2p}-gon. Here, p is infinity, and for all intents and purposes, p=2p.

The second figure shows what happens when a 90-degree rotation is applied to one of the squares - here, the one in the centre. It has now strangely lost its original {3,oo} symmetry, and acquired a new, {4,oo} symmetry. The thing can be regarded as a t{;oo;4} with each of the apeirogon-faces capped with a cupola.

The next figure shows half of the apeirogons rotated by one side. There are now lines of three squares, and the overall symmetry is that of an {oo,oo}.

The final frame shows what happens when the second half are rotated. The original rr{;3,oo;} in the first frame disappears, and we are left with something with alternating crosses of squares, and diamonds of triangles.

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