The genesis story begins with a single polyhedron with an ability to beget a dual, an inverse self or alter ego. We are free to play with the terms. Overly rigid formalisms need not predominate. Just the tetrahedron with this operation is able to beget another, and here our second operation is introduced: the combination of duals to create yet another polyhedron. The three all-triangles shapes form a kind of backbone.
A computer game just playing on these two operations with this simple beginning could take us into a plenitude of complicated multifaceted shapes in a hurry. However, even in the earliest of generations, combining the Platonic Five, we get our rhombics: dodecahedron (12 diamond facets); triacontahedron (30 diamond facets).
The cube itself is also rhombic, taking a square as a subset of rhombus. The dual of the rhombic dodecahedron is the cuboctahedron, so just out of the gate, we have the grist we need for our mill.
Here we distill the polyhedrons into a canonical structure, with the self-intersecting tetrahedron at the middle. Twelve balls around a nuclear ball in a cuboctahedral conformation sets the stage. Successive layers of 12, 42, 92, 162 balls, cuboctahedrally conformed, gives us entre into the micro world of crystals and viruses. The twist of a cuboctahedron's shell to become icosahedral is part of our STEM vocabulary of visualizations.
1, 12, 42, 92, 162...The need for a tetrahedral unit of volume, in relation to the canonical structure, the concentric hierarchy, helps motivate another use for the dam.
The dam is a subject of many open / closed source animations as our job as STEM teachers is to impart the basics of electricity generation. The energy per time of the powerhouse, the generators, their wattage, will be a topic of many segments.
In this other use though, the dam is presented as a collaborate project between ETs and Earthlings. The ETs are a source for our tetrahedral unit volume idea and bridging the cultures becomes and excuse for investigation foundational mathematics questions, thereby opening a door to philosophy.
Notions of work, energy, power, distance, momentum and time get a somewhat Newtonian treatment. Current and currency get connected in STEM, per systems theory roots and influences. The caloric requirements of humans, and their wattage (work output), is studied, using a First Person Physics point of view.
