Hypercube Embeddings of Wythoffians
نویسندگان
چکیده
The Wythoff construction takes a d-dimensional polytope P , a subset S of {0, . . . , d} and returns another d-dimensional polytope P (S). If P is a regular polytope, then P (S) is vertex-transitive. This construction builds a large part of the Archimedean polytopes and tilings in dimension 3 and 4. We want to determine, which of those Wythoffians P (S) with regular P have their skeleton or dual skeleton isometrically embeddable into the hypercubes Hm and half-cubes 12Hm. We find six infinite series, which, we conjecture, cover all cases for dimension d > 5 and some sporadic cases in dimension 3 and 4 (see Tables 1 and 2). Three out of those six infinite series are explained by a general result about the embedding of Wythoff construction for Coxeter groups. In the last section, we consider the Euclidean case; also, zonotopality of embeddable P (S) are addressed throughout the text.
منابع مشابه
Note on Half-cube Embeddings
We establish some results on embeddings in half-cube graphs. They are motivated by M. Deza, M. Dutour Sikirić, and S. Shpectorov’s conjecture [1] concerning isometric embeddings of the skeletons of polytope Wythoffians in half-cube graphs.
متن کاملEmbedding ladders and caterpillars into the hypercube
We present embeddings of generalized ladders as subgraphs into the hypercube. By embedding caterpillars into ladders, we obtain embeddings of caterpillars into the hypercube. In this way we obtain almost all known results concerning the embeddings of caterpillars into the hypercube. In addition we construct embeddings for some new types of caterpillars.
متن کاملEmbedding Ladders and Caterpillars into
We present embeddings of generalized ladders as subgraphs into the hypercube. By embedding caterpillars into ladders, we obtain embeddings of caterpillars into the hypercube. In this way we obtain almost all known results concerning the em-beddings of caterpillars into the hypercube. In addition we construct embeddings for some new types of caterpillars.
متن کاملHypercube Embeddings and Designs
This is a survey on hypercube embeddable semimetrics and the link with designs. We investigate, in particular, the variety of hypercube embeddings of the equidistant metric. For some parameters, it is linked with the question of existence of projective planes or Hadamard matrices. The problem of testing whether a semimetric is hyper-cube embeddable is NP-hard in general. Several classes of semi...
متن کاملEmbeddings in Hypercubes
One important aspect of efficient use of a hypercube computer to solve a given problem is the assignment of subtasks to processors in such a way that the communication overhead is low. The subtasks and their inter-communication requirements can be modeled by a graph, and the assignment of subtasks to processors viewed as an embedding of the task graph into the graph of the hypercube network. We...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008