Penrose C4 Cartwheel

Penrose C4 Cartwheel
CAD model of a Penrose C4 cartwheel
Type	Mathematical
Rods	<815 ×
Spheres	361 ×
Author	Amafirlian 22:11, 5 August 2007 (UTC)

This is a placeholder for a Penrose C4 cartwheel. It is build using the property that if you build a triangular pyramid on top of two connected rods that are spanning an angle of 70°, the top sphere is directly above the point where the sphere of a penrose dart needs to be. By using two levels one can build a complete penrose tiling. Note that the central rod (grey in the model) is effectively a support rod.

There is just one problem. When you put 2 Penrose darts built this way together, the two pyramids cause steric problems. The smallest angle between the rods is about 43°. The solution is to remove some of the rods that clash.

Partial views

The real tiling

Image generated by Junaid Rashid

External Links

• Penrose kite and dart information
• Penrose Cartwheels

• Junaid Rashid's generated picture on flickr