Analysis

When you open an angle structure list for viewing, you will see a table with all of the angle structures in your list.

Above this table is a header displaying the total number of angle structures. If you enumerated taut structures only, this will be reported in the header also:

Otherwise the header will indicate whether or not the convex span of these angle structures contains any strict and/or taut structures (these terms are defined below).

Details of Individual Angle Structures

Each row of the table represents a single angle structure in this list.

The leftmost column is used to indicate special types of angle structure. Possible values include:

Strict

Indicates a strict angle structure (all of its angles are strictly between 0 and π).

Taut

Indicates a taut angle structure (all of its angles are equal to either 0 or π).

If an angle structure is neither strict nor taut, the leftmost cell will be left empty.

The remaining columns list the individual angles that are assigned to edges in tetrahedra. These columns are labelled 0:01/23, 0:02/13, 0:03/12, 1:01/23, etc., where column t:ab/cd represents the angle assigned to tetrahedron t along the edge that joins tetrahedron vertices a and b, as well as the (opposite) edge that joins tetrahedron vertices c and d. Here 0 ≤ t < n, and a,b,c,d are some permutation of 0,1,2,3.