The basic shape of a BafaBall^TM is a dodecahedron, a twelve-faced polyhedron. The BafaBall^TM demonstrates 5-fold symmetry around axes through the centers of the pods, 3-fold symmetry around axes through the centers of triangular holes between pods, and 2-fold symmetry around axes through the Velcro-brand connectors. The numbers beneath the axis names show how many of the given axes can be found on a BafaBall^TM.

5-fold axis	3-fold axis	2-fold axis
6	10	15

If a circle perpendicular to an axis of symmetry is drawn on the surface of a BafaBall^TM with its center at the center of the BafaBall^TM, it forms a great circle which divides the ball into halves. These two halves are mirror images of each other at the same number of positions as the fold of the axis. If all of these great circles were drawn on the surface of a BafaBall^TM, they would form the pattern below on the surface of all pods. You can try this by wrapping a ball with three colors of ribbon.

So what is special about BafaBall^TM
that makes it a safe, sturdy toy?

BafaBall^TM use air pressure to distribute tension through a skin of nylon fabric. This nylon fabric is very tough. So tough that a 200 lb. person can jump on a BafaPod without bursting it. Inside the nylon fabric is an incredibly light air bladder that is made of aluminized nylon film. This type of balloon is actually used to hold helium, so holds air very well. Much, much, better than standard latex balloons. So when a person jumps on a BafaPod, the stress is distributed by the balloon to the tough nylon fabric cover all over the surface. This distribution of the work load- bladder to hold air, cover to take load - is the secret of BafaBall's ability. This allows each pod to handle large loads with ease.

By making our ball so light weight, we increase the safety. Watching our weight does make us susceptible to puncture. We do include two replacement balloons, should your ball meet a rosebush, but by being weight-conscious we've avoided the hazard of a heavy ball that could knock someone over. BafaBall^TM gives all the light weight fun of a balloon in a rugged package that can last and last. Just stay out of the roses.

"Why are these pods firmer at the center than at the rim?"

The research of Frei Otto has shown that under equal pressure, the surface of an inflatable structure is under greater tension where the radius of curvature is larger.

In other words, where the pod is flatter, it will feel firmer.

"Then, why are there wrinkles at the seam?"

At the seam, the forces parallel to the seam are very small compared to the forces perpendicular to them, so they wrinkle. We could have taken small darts of fabric out at the rim, but this would have dramatically increased cost without improving play value.

Why do BafPods change in firmness when the temperature changes?

Well, BafaPods are typically inflated to less than 2 psi, since they are inflated by mouth. This means that they are not inflated real hard, like a basketball. When the temperature drops, the air molecules slow down, and do not impact the balloon as forcefully, so the pod softens. When the temperature rises, the air molecules skitter around like mad,and karoom forcefully off of the walls, making the pods firmer.

For a basketball, the same changes take place, but they are less noticeable, since the ball is inflated far beyond the minimum needed to hold shape. We've elected to go the low pressure route to improve safety and fun.

Two principles work together making the BafaBall^TM a safe, sturdy toy:

1. Surface tension (firmness of the pod surface) rises as the radius of curvature of the pod increases. This causes the pill shapped pods of BafaBall^TM to be firmer at the center (where the radius of curvature is large) and softer at the rim (where the radius of curvature is less).
2. Surface tension rises with pressure, and pressure rises with temperature causing the pods to be firmer when warm than when cold

BafaBall^TM was inspired by the work of two
great scientists: Buckminster Fuller and Frei Otto.

Fuller and a sculptor named Snelson worked out the principles of tensegrity, which make visible the forces, which make a balloon a structure. In the case of BafaBall^TM, each balloon acts as a tensegrity, with the balloon and cover acting as a continuous tensional web, and the gas molecules within the balloon acting as discontinuous compressional members. When a BafaBall^TM is created, it also is a tensegrity structure, with tension made continuous by the Velcro-brand connectors. To learn more about tensegrity, you may want to purchase TensegriToy by Design Science Toys and the book "A Fuller Explanation" by Amy Edmondson, a good introduction to Fuller's tensegrity.

Frei Otto worked out many of the design principles behind tensional and inflatable structures. His research developed some of the basic theory behind inflatable structures from work with soap bubbles. For BafaBall^TM, Otto's work shows that the reason wrinkles develop at the seam of a BafaPod is that tensional stress parallel to the seam is zero. His book, "Tensile Structures, Volume 1", gives a full explanation of this phenomenon and is a wonderland of inflatable structures.

Learning by Play

During Active and Quiet play with BafaBall, many things are experienced: stable vs. unstable configurations - the power of the triangle, power of the sphere, color patterns, and the importance of symmetry. These concepts are learned by direct experience, giving the opportunity for deep understanding. We think you will find BafaBall^TM to be the perfect mixture of science and play.

As you learn - share! Write us! We love to see new examples of what can be done and learned with BafaBall^TM. Send us e-mail! at www.bafatoy.com .