Polyhedral Discretizations

...is an active science project and is 50% complete.
From tsbertalan on the 1st of January, 2012, at 6:54 am.

I am working with the lab of Dr. Eric Carlson on enhanced discretization schemes for simulating flow in porous media (that is, macro-scale pressure-driven flow of oil, gas, and water through underground reservoirs on the order of kilometers in linear dimensions).

For demonstration purposes, simulations often use a regular grid of cubic volume elements for these simulations—each element communicates with only six neighbors. However, each element actually has 26 neighbors (at the six faces, twelve edges, and eight corners). While there are polyhedra with 26 faces, they do not pack closely.

So, we're focusing on the truncated octahedron and the rhombic dodecahedron.