Twenty tetrahedrons share a common center point and represent the greatest number of tetrahedrons sharing a centerpoint within quantum-or-imperfect geometries. There are ten tetrahedrons outlined in orange and ten outlined in purple dots. On each side, then are five tetrahedrons outlined in those purple dots for a total of twenty tetrahedrons, all with gaps that could open or close.
Icosahedron: 20 tetrahedrons with gaps, all around a common centerpoint
We also call this gap geometry, imperfect geometry, quantum geometry or squishy geometry.
Fifteen objects share a center point using a five-octahedral cluster, five-tetrahedral cluster with another five. Also, with twenty tetrahedrons there can be three groups of five tetrahedrons that leaves a small group of four and a single tetrahedron.
Name this object.
We stumbled onto this configuration of the five-tetrahedral units over a five octahedral unit over a five tetrahedral unit. At what point it could manifest in physical reality is an open question. The function of such a thing is also an open question. I have asked around the geometry community and apparently it has no name.
It would be fun to see if we can construct this object with all the most popular interactive geometry software (IGS) and the dynamic geometry environments (DGEs) that are created.
