کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4656540 1343442 2006 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
New polytopes from products
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
New polytopes from products
چکیده انگلیسی

We construct a new 2-parameter family Emn, m,n⩾3, of self-dual 2-simple and 2-simplicial 4-polytopes, with flexible geometric realisations. E44 is the 24-cell. For large m,n the f-vectors have “fatness” close to 6. The Et-construction of Paffenholz and Ziegler applied to products of polygons yields cellular spheres with the combinatorial structure of Emn. Here we prove polytopality of these spheres. More generally, we construct polytopal realisations for spheres obtained from the Et-construction applied to products of polytopes in any dimension d⩾3, if these polytopes satisfy some consistency conditions. We show that the projective realisation space of E33 is at least nine-dimensional and that of E44 at least four-dimensional. This proves that the 24-cell is not projectively unique. All Emn for relatively prime m,n⩾5 have automorphisms of their face lattice not induced by an affine transformation of any geometric realisation. The group Zm×Zn generated by rotations in the two polygons is a subgroup of the automorphisms of the face lattice of Emn. However, there are only five pairs (m,n) for which this subgroup is geometrically realisable.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 113, Issue 7, October 2006, Pages 1396-1418