Gaps: The five-tetrahedral gap is the same as the five-octahedral gap.

by Bruce E. Camber

Nashville: In May 2022 after ten years of using these clear plastic models of tetrahedrons and octahedrons, the question was asked, “What happens when five octahedrons share a common center point?” The miracle of that moment is that because the five tetrahedral gap was very-well known and documented by many over the centuries, it felt significant, yet there appeared to be no analysis and no articles about this five octahedral configuration.

The open question is, “Where might this combination first manifest within space-time?” That opens more questions, “Could these five tetrahedrons then be covered by five more octahedrons? How far might it go on? How many could be stacked? Is there a maximum? What might such a configuration do? What might be its functionality?” In this model it is assumed that every possible geometric configuration manifests as something.

The next iteration is five tetrahedrons, five octahedrons, five tetrahedrons sharing a center point.

Five tetrahedrons over five octahedrons over five tetrahedrons
Possibly it could be called a triantahedron.


Does it have a name? In July 2022, we asked the question, “Does it have a name?” Nobody seemed to know. So, on November 22, stopping for lunch in the little town of Unadilla, Georgia in a little Subway sandwich shoppe, I was telling Hattie how no scholars had a name for the object. She asked, “How many sides does it have?” As you can see, it is not a straight-forward answer. Within our squishy geometry where the gap could be eliminated, I said, “20.” I should have said, 30, trianta. On February 1, 2023, it became informally known as the triantahedron. It is defined by fifteen objects (five octahedrons and ten tetrahedrons, and by the 7.35610+ degree gap which creates two more faces. Using squishy geometry, those two faces close up and become an edge.