Abstract
In the classical setting, a convex polytope is called semiregular if its facets are regular and its symmetry group is transitive on vertices. This paper continues our study of alternating abstract semiregular polytopes $$\mathcal {S}$$ . These structures have two kinds of abstract regular facets $$\mathcal {P}$$ and $$\mathcal {Q}$$ , still with combinatorial automorphism group transitive on vertices. Furthermore, for some interlacing number $$k\geqslant 1$$ , k copies each of $$\mathcal {P}$$ and $$\mathcal {Q}$$ can be assembled in alternating fashion around each face of co-rank 2 in $$\mathcal {S}$$ . Here we focus on constructions involving interesting pairs of polytopes $$\mathcal {P}$$ and $$\mathcal {Q}$$ . In some cases, $$\mathcal {S}$$ can be constructed for general values of k. In other remarkable instances, interlacing with certain finite interlacing numbers proves impossible.
Published Version
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