Background: This page was first posted in 2001 within our television series which ran from 1994-2012. It was our first public foray into geometry. The article was introduced:

“There are obvious facts – not just ideas  –  that could stimulate a child’s natural creativity simply because these facts exercise part of the brain that engages spatial-temporal relations in basic ways.  These all seem to be “basic-basics” that do not have much currency within education today. – Bruce Camber”

We all want the best for our children.  What if we were missing a few key steps in their education?  What if we missed a few key steps within our own education?  Perhaps engaging the following three simple facts are a little like listening to Beethoven before one learns how to speak.  All of us might benefit by exercising one’s brain in ways that  expand one’s commonsense logic structure.  More…

Fact #1:  A most-basic, three-dimensional object in space-and-time is the tetrahedron.
We all should know the object very well. Some adults may be a little familiar with the object, but generally it has no particular importance. It should. It is one of the most basic building block of the sciences.

Children should play with tetrahedrons and octahedrons as well as other kinds of building blocks and balls.

Now here is a postulate; it is also one of the most basic building block of epistemology and heuristics.

Fact #2:  Most adults cannot tell you what is perfectly enclosed within the tetrahedron.
This is not just a lack of insight into geometry, it is a lack of insight into the basic structures of biology, chemistry and physics. Look at the tetrahedron on the left. There are four tetrahedrons within each corner. The center face (yellow) is one of the four exterior faces of an octahedron. Its other four faces are interior. This image comes from the television series back in 1997 when we were trying to model “People, Products, and Processes” of business.  Now about that object identified in the center, the octahedron, it is magical.

Fact #3:  The octahedron is another most basic three-dimensional object, needs more attention.
From the octahedron we start seeing squares for the first time.  Yes, the ubiquitous square is derivative.  Now most scientists, logicians, and geometers cannot tell you what is perfectly enclosed within the octahedron.

That is a profound educational oversight.

Within each corner there is an octahedron.  There are six corners.  With each face is a tetrahedron.  There are eight faces.  The tape inside define four hexagonal plates that share a common center point.  Notice the tape comes in four different colors.

The internal structure of the octahedron is simple but opens the way to complexity quickly.  By making it a practice to look inside basic structure,  the mind gets exercised in very special ways.  Quickly, this simplicity-that-is-complexity becomes metaphorical.  The mind begins seeing similarities, analogies, and metaphors everywhere.  The mind begins making the strange familiar and the familiar strange. By going inside the octahedron one learns basic order, then basic relations that become functions that move the mind further within the interior world. More…