Beschreibung
A veering tetrahedron is a special kind of Taut tetrahedron, where the edges are coloured. This ensures some kind of global structure when constructing the Transverse veering triangulation.
Definition
A veering tetrahedron is a Transverse taut tetrahedron fulfilling the following properties:
- The colours of the equitorial edges alternate between red and blue
- Viewing any face from outside and following the edges anti-clockwise a non-equitorial edge is always followed by a red equitorial edge. The non-equitorial edges might be either red or blue.
Sometimes, the red edges are called right-veering and the blue edges left-veering. Ifthe two non-equitoriall edges are red (blue) the tetrahedron is called a red (blue) fan tetrahedron. If the edges differ, we call the tetrahedron a toggle tetrahedron.
The types determine how the tetrahedra can be glued to oneanother. If lower non-equitorial edge is red then the lower faces have two red faces and one blue face. This means that they can only be glued to an upper face whose non-equatorial edge is red. From this follows that red fan tetrahedra cannot be glued to blue fan tetrahedra.
Eigenschaften
Eigenschaft