Dihedral Closed Subsets of Finite Valency

Throughout this section, (L) is assumed to have finite valency. 

Assuming (L) to have finite valency we obtain that (L) is finite, so that, according to Lemma 10.1.7, L is spherical. 

Lemma 10.6.1 Let h and k be elements in L such that h=f= k, and assume (L) to have finite valency. Let R be the set of all elements s of S such that s) d. Then the following hold. 

The values nr u) are computed similarly. This proves the lemma. 

We are assuming (L) to have finite valency. As a consequence, (L) is a finite set. In particular, ((L)) has a maximal element. In the following, we shall denote this element by max ((L)). 

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