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The Assembly Problem for Alternating Semiregular Polytopes
Discrete & Computational Geometry ( IF 0.8 ) Pub Date : 2019-08-14 , DOI: 10.1007/s00454-019-00118-6 Barry Monson , Egon Schulte
Discrete & Computational Geometry ( IF 0.8 ) Pub Date : 2019-08-14 , DOI: 10.1007/s00454-019-00118-6 Barry Monson , Egon Schulte
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 $$\mathcal {S}$$ S . These structures have two kinds of abstract regular facets $$\mathcal {P}$$ P and $$\mathcal {Q}$$ Q , still with combinatorial automorphism group transitive on vertices. Furthermore, for some interlacing number $$k\geqslant 1$$ k ⩾ 1 , k copies each of $$\mathcal {P}$$ P and $$\mathcal {Q}$$ Q can be assembled in alternating fashion around each face of co-rank 2 in $$\mathcal {S}$$ S . Here we focus on constructions involving interesting pairs of polytopes $$\mathcal {P}$$ P and $$\mathcal {Q}$$ Q . In some cases, $$\mathcal {S}$$ S can be constructed for general values of k . In other remarkable instances, interlacing with certain finite interlacing numbers proves impossible.
更新日期：2019-08-14
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