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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 reflection. Use this Polypad to create the Sphinx tiling. As you do,

  • Determine the total number of triangles and the number of sphinx tiles needed to create each figure.

Sphinx tiles can be used to create fractals.

  • Create your own design.
  • Determine 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

Use this Polypad to create more reptiles using these shapes;

Polypads for This Lesson

To assign these to your classes in Mathigon, save a copy to your Mathigon account. Click here to learn how to share Polypads with students and how to view their work.

polypad.org/TTxBb4kmMgprXA
polypad.org/wsnlk42d6Z9pw
polypad.org/WrDeJHYRc3CUwg

Desmos Classroom Link

teacher.desmos.com/activitybuilder/custom/6376c04af03a56dc66180cd4