**Quantum geometries**: **A polyhedron with 20 faces, one of the five Platonic solids**, there are many historical studies. The focus 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 single. In another configuration there are two groups of five and a ring of ten separating them. Notwithstanding, there is rotational symmetry.

Taken all together students called it, “Squishy geometry.” And, it is!

In the high school, we suggest to the students that it may be part of the beginning of *quantum geometries* within quantum physics. Pictured here on the left is a group of five tetrahedrons bound by red plastic tape. The magnetic balls remind us that no space is actually “empty”and that singularities exist on paper only.

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In this second image or five tetrahedrons, bound by blue tape, we 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.

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With this third image, 15 of the 20 tetrahedrons have been displayed. In this image you can see through the clear plastic tetrahedrons — there are reflections of the five bound by red at the top and reflections of the blue on the bottom right. That leaves five more tetrahedron to find.

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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 eventually be studying it closely.

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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 may be 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.

There is also a study of the tetrahedron, the octahedron, harmony and their combinations.

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