4D-POLYTOPES AND THEIR DUAL POLYTOPES OF THE COXETER GROUP W(A4) REPRESENTED BY QUATERNIONS
نویسندگان
چکیده
منابع مشابه
Essential Hyperbolic Coxeter Polytopes
We introduce a notion of essential hyperbolic Coxeter polytope as a polytope which fits some minimality conditions. The problem of classification of hyperbolic reflection groups can be easily reduced to classification of essential Coxeter polytopes. We determine a potentially large combinatorial class of polytopes containing, in particular, all the compact hyperbolic Coxeter polytopes of dimens...
متن کاملCoxeter matroid polytopes
If ∆ is a polytope in real affine space, each edge of ∆ determines a reflection in the perpendicular bisector of the edge. The exchange group W (∆) is the group generated by these reflections, and ∆ is a (Coxeter) matroid polytope if this group is finite. This simple concept of matroid polytope turns out to be an equivalent way to define Coxeter matroids. The GelfandSerganova Theorem and the st...
متن کاملVolume, Facets and Dual Polytopes of Twinned Chain Polytopes
Let P and Q be finite partially ordered sets with |P | = |Q| = d, and C(P ) ⊂ R and C(Q) ⊂ R their chain polytopes. The twinned chain polytope of P and Q is the normal Gorenstein Fano polytope Γ(C(P ),−C(Q)) ⊂ R which is the convex hull of C(P )∪(−C(Q)). In this paper, we study combinatorial properties of twinned chain polytopes. First, we will give the formula of the volume of twinned chain po...
متن کاملCoxeter n - polytopes with n + 3 facets
We use methods of combinatorics of polytopes together with geometrical and computational ones to obtain the complete list of compact hyperbolic Coxeter n-polytopes with n + 3 facets, 4 ≤ n ≤ 7. Combined with results of Esselmann [E1] this gives the classification of all compact hyperbolic Coxeter n-polytopes with n + 3 facets, n ≥ 4. Polytopes in dimensions 2 and 3 were classified by Poincaré [...
متن کاملOn simple ideal hyperbolic Coxeter polytopes
Let IH be the n-dimensional hyperbolic space and let P be a simple polytope in IH. P is called an ideal polytope if all vertices of P belong to the boundary of IH. P is called a Coxeter polytope if all dihedral angles of P are submultiples of π. There is no complete classification of hyperbolic Coxeter polytopes. In [6] Vinberg proved that there are no compact hyperbolic Coxeter polytopes in IH...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Geometric Methods in Modern Physics
سال: 2012
ISSN: 0219-8878,1793-6977
DOI: 10.1142/s0219887812500351