Polymorf - Knowhere - Two-dimensional stability

to the extreme pressure underground, let alone be useful for building mountains, trees, or

houses for little pigs above ground. Structural materials get their strength and stability from

the way that their atoms (i.e. bricks) are packed together (i.e. stacked) by the force of their

atomic bonds (i.e. mortar) so as to resist being pushed out of shape by external forces (i.e.

wolf puffs). The reason an element like carbon can be soft and flaky like the graphite in a

pencil, and yet hard and brittle like diamond, is due solely to the way the carbon atoms

are arranged structurally. That is, certain structures are inherently more stable than others

regardless of what they are made of. This will be demonstrated in the following section.

Two-dimensional stability

For example, build a chain made from six small square (SS) Polymorf panels that are

joined together by flexible pin hinges, or pinges. The chain is obviously not very stable


Fig. 119 - Six member flexible chain
with hingeable joints
(demonstration model)

since both ends of it and the middle can be moved in any direction with the slightest push.

The only restriction is that the individual members are linked together. Now join the ends

of the chain together forming a six-member hexagonal ring. Notice that the ends of the

	chain are no longer free to move independently of each other
	and the movements of the individual members are confined to
	the ring's perimeter. But the hexagon is still very flexible.
	Very little force is required to move the members and distort
	the hexagon's shape.

	◄ Fig. 120 - Flexibility of a hexagon. (demonstration model)

Next remove one of the members from the ring and then pin the free ends of this five-

member chain back together forming a pentagon. The pentagon is still pretty flexible but

	the movement of the individual members is
	more restricted than before. Remove another
	member forming a four-member parallelogram.
	This shape still flexes but opposite members can
	only move parallel to each other. Finally remove
	another member forming a triangle. This shape
	is now stable! Since the individual members of
Fig. 121 - Flexibility of polygons with	the triangle are held together by pinges, its
decreasing number of members.	stability can only be due to two things - the
(demonstration models)	rigidity of the individual members and the

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