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Once you have built a list of surfaces, you can study these surfaces using the various tabs in the normal surface list viewer.
Above all of these tabs is a header displaying the total number of surfaces and the original enumeration parameters (i.e., the coordinate system you selected, and whether or not you asked for embedded surfaces only).
If the header says that you enumerated in legacy almost normal coordinates, it means that the list was created using Regina 4.5.1 or earlier, and that surfaces with more than one octagon were deleted. See the discussion on legacy coordinates for details.
The Summary tab breaks the total count into sub-counts for different types of surfaces, as illustrated below. At a broad level, the total is divided into closed surfaces, bounded surfaces (which have only real boundary), and spun normal surfaces (which have infinitely many triangles). For each category that contains one or more surfaces, a table is given to break this down further according to orientability, 1-or-2-sidedness, and Euler characteristic.
If the coordinate system that you used for enumeration does not support spun normal surfaces, they will not be listed here in the Summary tab.
You can view details of the individual surfaces in the Surface Coordinates tab. This brings up a large table in which each row represents a single normal (or almost normal) surface.
Above the table are some drop-down boxes that let you view the list in different ways. These are discussed further in the notes on coordinate systems and filtering surfaces.
In the first column, surfaces are numbered 0,1,2,... (in no particular order) so that you can make note of them for later on. You can also assign arbitrary names to surfaces by typing directly into the second column; these names will be saved with your data file.
The next few columns describe various properties of each surface. Some of these columns might be empty or absent in your viewer (for instance, Regina does not compute Euler characteristic for spun normal surfaces, and it hides the orientability column if your enumeration allowed for immersed or singular surfaces).
The columns and their meanings are:
Shows the Euler characteristic of the surface.
Contains a tick (✓) if the surface is orientable, or the text Non-or. if it is not.
Shows whether the surface is one-sided or two-sided.
Indicates what type of boundary the surface has. This will be one of:
Indicates a closed, compact surface (i.e., no boundary at all and finitely many discs).
Indicates a compact surface with boundary (i.e., finitely many discs, some of which meet the boundary of the triangulation).
Indicates a spun normal surface (i.e., a non-compact surface with infinitely many discs). These only appear when the enumeration is done in quadrilateral or quadrilateral-octagon coordinates.
Indicates if a surface is a vertex link or a thin edge link (i.e., the boundary of a small regular neighbourhood of a vertex or edge). If this is a one-sided surface whose double is a thin edge link, then it will be reported as a thin edge link for these purposes.
The relevant vertex or edge will be listed also, using the vertex and edge numbers that appear in the first column of the vertex viewer and edge viewer. It is possible for a surface to be the thin edge link for two edges at the same time, in which case both edges will be listed.
If the surface is not a vertex link or a thin edge link, this cell will be left empty.
Indicates if this is one of a few special types of surface that Regina identifies. Possible values are: