occasional meanderings in physics' brave new world
- Name: Kea
- Location: New Zealand
Marni D. Sheppeard
Tuesday, April 08, 2008
Note that an intersection on the triangle plane arrangement becomes a square face on the cube. A (directed) cone from the top vertex will pick out the central horizontal edge of the cube, with the central point of the hexagon at one end representing the triangle. Observe that the number of edges in corresponding diagrams (planar arrangements to graphs) remains unchanged, whereas faces become vertices and vertices become faces. That is, this is a kind of Poincare duality.