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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Page 78 - Building Stability - Two-dimensional stability

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