A polyhedron with 20 faces, one of the five Platonic solids, there are many historical studies. The focus here is on the imperfect, the geometric gaps of the twenty tetrahedrons, extended here (five images below) as three groups of five, a group of four and singlet. In another configuration there are two groups of five and a ring of ten separating them. Notwithstanding, there is rotational symmetry.
Taken all together we tell the school children, “It’s squishy geometry.” And, it is! In the high school, we suggest to the students that it is part of the beginning of quantum geometries and quantum physics. Pictured here on the left is a group of five tetrahedrons bound by red plastic tape. The magnetic balls within each tetrahedron is just to remind us that there is no space that is “empty.” And, I’ll go so far as to suggest that there is also no singularity.
In this second image or five tetrahedrons, bound by blue tape, you can see part of the five tetrahedrons bound by red (above) through the clear plastic. There are in fact 20 tetrahedrons all bound together. They all share a common centerpoint. The next image of five are bound by a dark green plastic tape.
With this image, 15 of the 20 tetrahedrons are displayed. In this image you can see through the clear plastic tetrahedrons, there are reflections of the five bound by red at top and reflections of the blue on the bottom right. That leaves five more tetrahedron to find.
We find a cluster of of four tetrahedrons, here bound by clear tape and you can see wisps of the red, blue and green groups on the edges. This four-and-one configuration (the one being just below) with the three groups of five tetrahedrons harbors a special type of asymmetry and discontinuity. We’ll be studying it closely.
Yes, and finally, very clearly, all by itself, is a solitary tetrahedron. The red, blue and green tape of the abutting tetrahedral sets are readily discerned.
The icosahedral cluster (of twenty tetrahedrons) just maybe considered a transformational nexus and in future articles, that concept will be explored further.
There are many references to the icosahedron within this site. Use the “Find” function (CMD F) and enter “icosahedron” to go to each reference more quickly.
Coming up: A study of pi electrons