Uniform edge-c-colorings of the Archimedean tilings
نویسندگان
چکیده
In the book Tilings and Patterns by B. Grunbaum and G. S. Shephard, the problem of classifying the uniform edge-c-colorings of Archimedean tilings of the Euclidean plane is posed. This article provides such a classification.
منابع مشابه
Tiling with Regular Star Polygons
The Archimedean tilings (Figure 1) and polyhedra will be familiar to many readers. They have the property that the tiles of the tiling, or the faces of the polyhedron, are regular polygons, and that the vertices form a single orbit under the symmetries of the tiling or polyhedron. (Grünbaum and Shephard [1] use Archimedean, in relation to tilings, to refer to the sequence of polygons at each ve...
متن کاملSelf-assembly of Archimedean tilings with enthalpically and entropically patchy polygons.
Considerable progress in the synthesis of anisotropic patchy nanoplates (nanoplatelets) promises a rich variety of highly ordered two-dimensional superlattices. Recent experiments of superlattices assembled from nanoplates confirm the accessibility of exotic phases and motivate the need for a better understanding of the underlying self-assembly mechanisms. Here, we present experimentally access...
متن کاملComplex Archimedean tiling self-assembled from DNA nanostructures.
Archimedean tilings are periodic polygonal tessellations that are created by placing regular polygons edge-to-edge around a vertex to fill the plane. Here we show that three- and four-arm DNA junction tiles with specifically designed arm lengths and intertile sticky-end interactions can be used to form sophisticated two-dimensional (2D) and three-dimensional (3D) tessellation patterns. We demon...
متن کاملMinimal Covers of the Archimedean Tilings, Part II
In Part I of this paper ([PW12]), the minimal regular covers of three of the eight Archimedean tilings were determined. However, the computations described in that work grow more complicated as the number of flag orbits of the tilings increases. In Part II, we develop a new technique in order to present the minimal regular covers of certain periodic abstract polytopes. We then use that techniqu...
متن کاملInfluence of Non-Uniform Wall Temperature on Local Heat Transfer Coefficient in a Rotating Square Channel
Abstract: This paper presents the results of an experimental examination of the effect of non-uniform wall temperature on local heat transfer coefficient in a rotating smooth-walled square channel. Three different thermal boundary situations were investigated: (a) even and odd (four) wall uniform temperature, (b) even and odd (four) wall uniform heat flux, and (c) even (leading and trailing) w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 338 شماره
صفحات -
تاریخ انتشار 2015