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A expansion joint, or movement joint, is an assembly designed to hold parts together while safely absorbing temperature-induced expansion and contraction of building materials. They are commonly found between sections of buildings , bridges , sidewalks , railway tracks , piping systems , ships , and other structures.
There are different notations for expressing these uniform solutions, Wythoff symbol, Coxeter diagram, and Coxeter's t-notation. Simple tiles are generated by Möbius triangles with whole numbers p,q,r, while Schwarz triangles allow rational numbers p,q,r and allow star polygon faces, and have overlapping elements.
The expansion joint hinges provide for angular movement and will resist pressure thrust forces. [4] Individual hinged expansion joints used in piping systems are restricted to pure angular rotation by its hinges. As a pair, hinged expansion joints will function together to absorb lateral deflection.
Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...
From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular octagonal tiling.. Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 10 forms.
In 1981, Grünbaum, Miller, and Shephard, in their paper Uniform Tilings with Hollow Tiles, list 25 tilings using the first two expansions and 28 more when the third is added (making 53 using Coxeter et al.'s definition). When the fourth is added, they list an additional 23 uniform tilings and 10 families (8 depending on continuous parameters ...
The standards are a combination of a variety of expansion joint manufacturers' knowledge and experience. [2] [3] The EJMA organization performs extensive technical research on a variety of topics concerning the design and manufacturing of expansion joints. [4] This knowledge contributes to providing new versions of the EJMA book of standards.
A Penrose tiling with rhombi exhibiting fivefold symmetry. A Penrose tiling is an example of an aperiodic tiling.Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches.