Hat
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Hat  

Rank  2 
Type  Einstein 
Elements  
Edges  14 (all distinct) 
Vertices  14 (all distinct) 
Measures (smallest edge length = 1)  
Perimeter  
Abstract & topological properties  
Flag count  28 
Orientable  Yes 
Properties  
Symmetry  I×I, order 1 
Flag orbits  28 
Convex  No 
Net count  7 
History  
Discovered by 

First discovered  2023 
The hat is a 14sided polykite, which along with it's mirror image can tessellate the plane, but only nonperiodically. This makes it a solution to some formulations of the einstein problem. It can be formed as an outerblend of eight 60°90°120°90° kites, or 4 mirrorsymmetric pentagons.
Two of its sides meet at an angle of π , making them appear as a single edge. However there must be a vertex at that location for the aperiodic tiling to work.
Vertex coordinates[edit  edit source]
Vertex coordinates for a hat with smaller edge length 1 can be given by:
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 .
Gallery[edit  edit source]

Divided into 8 kites.

A section of a tessellation of hats.
External links[edit  edit source]
 Smith, Myers, Kaplan, and GoodmanStrauss. An aperiodic monotile
 Weisstein, Eric W. "Hat Polykite" at MathWorld.