Einstein Tile - How to Construct an Aperiodic Monotile Using Inkscape (The Hat Tile)

The Hat Tile or Einstein Tile (aperiodic monotile)
The discovery of an "Einstein Tile" was announced on 20th March 2023. This is a single tile that will completely tile the infinite plane but cannot do so in a periodic manner. Such a tile is called an aperiodic monotile. Previously it was not known if such a tile existed.
The video puts this discovery in context by describing how it develops from the work of Roger Penrose and his discovery in the 1970s of the Dart and Kite - a set of two tiles that had the same property.
The video then shows how the tile can be constructed using Inkscape which is a free open source vector graphics software. You are taken through each step in detail.
The video finishes by showing how you can attempt to create a tiling with the tiles you constructed. This is a fun activity.
Inkscape can be downloaded from inkscape.org
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Chapters
0:00 Intro & Context
1:43 Inkscape preparation
3:38 Constructing the tile
10:14 Creating a set of 5 coloured tiles
12:19 How to start tiling
14:39 End links

Other videos in this series:
Using Inkscape to construct the Penrose Tiles (Part 1: Outline shape of the Kite and Dart) https://youtu.be/ru9MrsHaGAk
Using Inkscape to construct the Penrose Tiles (Part 2: Constructing the edge constraint patterns) https://youtu.be/yeSZfd8eu9U
Using Inkscape to construct the Penrose Tiles (Part 3: Exploring Penrose Tiling (Kites and Darts)) https://youtu.be/2LaM_cTinAs
Using Inkscape to construct the Penrose Tiles (Part 4: Inflating a Penrose Tiling (Kites and Darts)) https://youtu.be/h__oFu2T3Ig
Penrose Tiles Part 5 - Kites, Darts, Inflation, Fibonacci Numbers and the Golden Ratio https://youtu.be/vxgIM2Xaa3E