In your trek through Knowhere you have seen how the structure of space orders things

around.  It facilitates individual expression of form on the local level while maintaining

overall uniformity of composition on the extended level.


On the one hand, as you saw in Geometry rules, spatial ordering principles permit things

to have complementary mirror planes and axes of symmetry, similar surface and

volumetric relationships, congruent structural elements, and dual frameworks, to name

a few. This allows structures to be transformed into each other via truncation, sectioning

and rearrangement, compounding, and stellation operations.  Also structures can be

inscribed in each other and they can be packed together to fill space.  All of these

attributes are conducive to creating a rich mix of diverse forms that can inhabit space.


On the other hand, the structure of space limits diversity of form by invoking certain other

ordering principles that things must abide.   As you probably already know from geometry,

two-dimensional polygons and three-dimensional polyhedra must maintain a topological

balance between their vertices, edges, and faces.  And, as you saw in Building stability,

for polygons, polyhedra, lattices, and plate structures to be inherently stable they must

adhere to additional topological constraints.  Another purely geometrical limitation is  that

the sum of the interior or dihedral angles of polygons and polyhedra must be constant.

And the sum of the angles about a point must equal 360o, for example.  In structural terms,

the bearing capacity of beams and columns is limited by spatial considerations such as

their moment of inertia and their length.  And the strength of trusses and spaceframes

depends significantly on the ratio of their height, or depth, to their span.  All of these

factors limit the possible forms that things can take.
Taken as a whole, these abstract ordering principles provide the structural matrix within
which the dynamic interaction of physical forces are played out in the real world.  In
Structure matters, you saw how the crystal lattice structure accommodates the attractive
and repulsive forces of atoms of different size, ligancy, and charge so that they can pack
together uniformly into elements and minerals.  Building stability demonstrated that the
omni-triangulated two-dimensional truss structure permits the internal forces induced by
external loads to be exactly and intimately balanced by aligning them axially.  Likewise,
the three-dimensional spaceframe framework can bear a load perpendicular to its plane by
dissipating the resulting forces axially among its members by means of lattice action.  The
stability of a plate structure is due to the fact that its plates can dissipate internal forces
across the entire surface of the plate, and concentrate them at its edges, as counter acting
shear stresses.  A lattice tower can dissipate its load throughout its omni-triangulated
framework.  And, Gizmoneering showed that machines can be engineered with different
combinations of rigid and moving parts to efficiently convert and transmit externally
applied forces into mechanical motion that can do work.
All of these structural systems owe their strength, stability, and efficiency in large part to
the structural properties of space.  Without these ordering principles existence might well
be relegated to either a diverse sand pile of non-uniform particles at one extreme, or a
single, uniform entity at the other.  Instead, because of these principles, we enjoy  a great
diversity of materials and structures that contribute substantially to our welfare and
security.   Indeed space is something else!


Back to Knowhere



home   sitemap   products   Polywood   .networks   contact us   Knowhere   3Doodlings