This great site developed by Ron Eglash gives a number of resources that engage with the principles of geometry.
1. Transformational geometry and iteration in Mangbetu Art – the art work shows the use of all four geomtric transfomational principles, Reflection, Translation, Rotation and Scaling. The link enables you to find out more about Mangbetu Art and use the software to simulate traditional designs or create your own new ones.
2. Transformational geometry and iteration in Cornrow hairstyles – Many new cornrow hairstyles demonstrate the use of four geometric principles; translation, rotation, reflection and dilation. You can find out how to braid but also use the free software to create new braid designs
3. Coming soon – Yupik Parka Patterns
Why not use these resources to explore the principles of geometry?