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Sphinx Tilings

Introduction

"Rep-tile" has a different meaning in Mathematics It is short for Replicating Tile. When several copies of these tiles are put together, the shape will appear exactly the same but magnified! Every square, rectangle, parallelogram, rhombus, or triangle are examples of rep-tiles. Let's explore some other ones.

Sphinx Tiles

Sphinx Tiles are one of the most popular rep-tiles and are made from 6 equilateral triangles.

To create the same Sphinx shape, we need to use the original shape and its mirror-image.

Use the flip button of the Polypad to create the mirror image. This is also called a reflection. Use this canvas to create the Sphinx tiling. As you do, think about the number of sphinx tiles needed to create each figure and the total number of triangles needed to create each figure.

Sphinx tiles can be used to create fractals too. Find the scale factor to create the next sphinx tile. Then iterate the fractal one more step. Figure out the transformations that create this fractal.

Extensions

Can you use the shapes below to make larger copies of the same shape?