List of k-uniform tilings

Example <i>k</i>-uniform tilings<table><tbody><tr><td>1-uniform (regular)</td><td>1-uniform (semiregular)</td></tr><tr><td>2-uniform tiling</td><td>3-uniform tiling</td></tr></tbody></table>
<p>A <i>k</i>-uniform tiling is a tiling of <a href="/facts/Tessellation/7BWDywXC">tilings</a> of the plane by convex <a href="/facts/Regular_polygon/ws89Nhpt">regular polygons</a>, connected edge-to-edge, with <i>k</i> types of vertices. The 1-uniform tiling include 3 regular tilings, and 8 semiregular tilings. A 1-uniform tiling can be defined by its <a href="/facts/Vertex_configuration/wWaBS6t0">vertex configuration</a>. Higher <i>k</i>-uniform tilings are listed by their vertex figures, but are not generally uniquely identified this way.
</p><p>The complete lists of <i>k</i>-uniform tilings have been enumerated up to k=6. There are 20 2-uniform tilings, 61 3-uniform tilings, 151 4-uniform tilings, 332 5-uniform tilings, and 673 6-uniform tilings. This article lists all solutions up to <i>k</i>=5.
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<p>Other <a href="/facts/Euclidean_tilings_by_convex_regular_polygons/tR5CQACy">tilings of regular polygons that are not edge-to-edge</a> allow different sized polygons, and continuous shifting positions of contact.
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List of k-uniform tilings open-in-new

List of k-uniform tilings