The question is asked, “Is this a new construction of a basic geometry?”

Five-tetrahedrons, five-octahedrons, five tetrahedrons and their gap
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 of the object. She asked, “How many sides does it have?” As you can see, it is not a straightforward answer. Within our squishy geometry where the gap would 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. For this naming, squishy geometry closed it up to be an edge.

Pages from which this image has been linked:

  1. An introduction to the geometries of the gaps
  2. Many scholars will be introduced to this construction.