Welcome to Regina!

A single Regina data file can store a range of objects, from 3-manifold triangulations and normal surfaces to Python scripts, PDF documents and text notes (such as the one you are reading now).

These objects are called "packets", and are arranged in a tree-like structure as you can see to the left. To view or edit a packet, just click on the packet in the tree (on some platforms, such as MacOS, you should double-click instead).

Have a play with the packets in this file to see what Regina can do.

If you ever want to know what some element of the user interface means (such as a button or a text box), just press Shift-F1 and click on the thing that you want to know more about. You can try this now with the tree in the main window, or the buttons in the toolbar. If you ever forget the Shift-F1 shortcut, you can find it in the menu under Help → What's This?

For more detailed help, try the Regina Handbook (in the Help menu, or just press F1). The handbook includes lots of screenshots and talks you through how to do many different things.

Any questions? Just mail the authors; see Help → About for our email addresses.

Enjoy!

- The Regina development team
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1 54 1 156 -1 -1 -1 -1
2 54 2 156 0 135 0 120
3 39 3 216 1 135 1 120
3 57 3 147 2 216 2 39

#

1 4 -1 -1 -1 -1
2 4 3 3 0 2
4 5 5 3 1 2
1 3 6 5 -1 -1
8 0 7 2 2 5
2 3 9 5 10 5
11 5 3 5 8 3
12 0 8 5 4 4
4 0 7 5 6 3
13 2 5 5 12 3
5 5 14 1 -1 -1
13 5 14 4 6 5
7 0 13 4 9 3
12 2 9 4 11 5
11 2 15 4 10 1
14 2 -1 -1 -1 -1
0 1 1 1 2 1 3 1 10 1 11 1 12 1 13 1 20 1 21 1 24 1 35 2
2 2 3 2 12 2 13 2 15 2 22 2 23 2 29 2 30 2 31 2 32 3 33 3 34 1
0 2 1 2 16 2 25 2 32 1 33 1 34 1
2 1 3 1 4 1 10 1 11 1 12 1 13 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
5 2 12 1 13 1 14 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
0 2 1 2 5 4 12 2 13 2 18 2 20 2 21 2 22 2 23 2 25 2 30 2 31 2 32 3 33 3 34 1
0 1 1 1 5 1 18 1 20 1 21 1 35 1
2 2 3 2 5 2 12 2 13 2 19 2 20 2 21 2 22 3 23 3 24 1 30 3 31 3 32 3 33 3
6 2 15 2 22 1 23 1 24 1 30 1 31 1 32 1 33 1
0 2 1 2 6 5 10 2 11 2 15 3 22 1 23 1 28 2 30 2 31 2 32 1 33 1 36 1
6 1 15 1 22 1 23 1 38 1
0 4 1 4 6 2 10 2 11 2 16 2 20 1 21 1 27 1 30 1 31 1 32 1 33 1
0 2 1 2 6 1 10 1 11 1 16 1 20 1 21 1 35 1
0 4 1 4 6 3 10 3 11 3 16 1 20 1 21 1 26 2 30 1 31 1 36 1
0 6 1 6 6 4 10 4 11 4 16 2 20 2 21 2 26 2 30 1 31 1 37 1
0 4 1 4 6 1 10 1 11 1 16 3 20 1 21 1 25 2 32 1 33 1 39 1
0 2 1 2 6 2 10 1 11 1 17 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
0 3 1 3 2 1 3 1 6 1 10 2 11 2 18 1 20 1 21 1 26 2 30 1 31 1 36 1
0 1 1 1 7 1 10 1 11 1 12 1 13 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
2 2 3 2 8 2 10 2 11 2 12 2 13 2 15 2 20 2 21 2 22 3 23 3 24 1 30 3 31 3 32 3 33 3
0 1 1 1 8 1 10 1 11 1 16 1 20 1 21 1 35 1
0 1 1 1 8 3 10 3 11 3 16 1 20 1 21 1 26 2 30 1 31 1 36 1
2 2 3 2 9 2 10 2 11 2 12 3 13 3 14 1 20 3 21 3 22 3 23 3 30 3 31 3 32 3 33 3
4 2 16 2 25 2 32 1 33 1 34 1
2 1 3 1 4 1 10 1 11 1 12 1 13 1 20 1 21 1 24 1 35 2
5 2 12 1 13 1 14 1 20 1 21 1 24 1 35 2
2 1 3 1 5 1 12 1 13 1 19 1 20 1 21 1 24 2 35 3
6 1 15 1 24 1 35 1
0 2 1 2 6 2 10 1 11 1 17 1 20 1 21 1 24 1 35 2
0 1 1 1 7 1 10 1 11 1 12 1 13 1 20 1 21 1 24 1 35 2
2 1 3 1 8 1 10 1 11 1 12 1 13 1 15 1 20 1 21 1 24 2 35 3
2 2 3 2 9 2 10 2 11 2 12 3 13 3 14 1 20 3 21 3 24 3 35 6
0 1 1 1 2 1 3 1 10 1 11 1 12 1 13 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
6 1 12 1 18 1 26 1
6 2 12 2 16 1 17 1 18 1 21 1 22 1 23 1 24 1
5 2 9 1 10 1 11 1 14 1 15 1 18 1 26 2
5 2 9 1 10 1 11 1 14 1 15 1 16 1 17 1 21 1 22 1 23 1 24 1
4 2 13 2 19 2 23 1 24 1 25 1
2 1 3 1 4 1 7 1 8 1 9 1 10 1 14 1 15 1 18 1 26 2
2 1 3 1 4 1 7 1 8 1 9 1 10 1 14 1 15 1 16 1 17 1 21 1 22 1 23 1 24 1
0 1 1 1 4 1 13 2 19 2 23 1 24 1 25 1
0 1 1 1 2 1 3 1 7 1 8 1 9 1 10 1 14 1 15 1 18 1 26 2
0 1 1 1 2 1 3 1 7 1 8 1 9 1 10 1 14 1 15 1 16 1 17 1 21 1 22 1 23 1 24 1
0 2 1 2 13 2 19 2 23 1 24 1 25 1
0 2 1 2 6 1 7 1 8 1 13 1 14 1 15 1 26 1
0 4 1 4 6 3 7 3 8 3 13 1 14 1 15 1 20 2 21 1 22 1 27 1
1 120 2 147 3 78 4 39
0 156 2 54 3 147 4 78
0 57 1 135 3 45 4 147
0 78 1 57 2 99 4 201
0 39 1 78 2 57 3 210

#

##

1 228 1 228 2 141 2 120
0 228 0 228 2 39 2 210
0 114 0 156 1 39 1 201

# 2

2

## 2

There are in fact two triangulations of this 3-manifold with three tetrahedra.
% Triangulation m129 geometric_solution 3.66386238 oriented_manifold CS_unknown

2 0 torus 0.000000000000 0.000000000000 torus 0.000000000000 0.000000000000

4 1 2 3 1 0132 0132 0132 3201 0 1 0 1 0 1 -1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 -1 1 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.000000000000 1.000000000000

0 0 3 2 0132 2310 3120 3120 0 1 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 -1 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.500000000000

1 0 3 3 3120 0132 0213 3120 0 1 1 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 -1 1 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.500000000000

2 2 1 0 3120 0213 3120 0132 0 1 1 0 0 -1 0 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 -1 1 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.500000000000

% Triangulation m004 geometric_solution 2.02988321 oriented_manifold CS_unknown

1 0 torus 0.000000000000 0.000000000000

2 1 1 1 1 0132 1230 2310 2103 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 0 -1 0 0 1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.866025403784

0 0 0 0 0132 3201 3012 2103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 -1 0 1 0 1 0 0 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.866025403784

1 0 2 3 2 1
0 0 3 1 3 5
0 3 0 1 4 2
1 5 5 0 1 1
2 4 6 1 6 5
7 3 3 0 7 5
4 5 7 2 4 1
5 5 5 3 6 4
0 1 1 1 2 1 3 1 7 1 8 1 9 1 10 1
0 2 3 1
2 2 3 1
1 1 4 2
1 1 5 2
1 1 3 1 6 1
2 1 5 1 6 1
0 1 4 1 6 1
0 1 2 1 3 2 6 2
1 2 4 1 5 1 6 2
0 17475 1 17496 1 17937 0 16593 1 10440
0 17986 1 13408 0 13576 0 17104 1 6352
0^1 1^2 0^-2 1^-3
1^2 0^3 1^-1 0^-2
0 13380 1 18056 1 18056 1 18056 0 2257
1 13380 0 18056 0 18056 0 18056 1 2257
10 1 25 1
2 1 7 1 11 1 17 1 22 1 26 1
1 1 2 1 3 1 8 1 16 1 17 1 18 1 23 1
0 1 4 1 5 1 14 1 15 1 19 1 20 1 29 1
0 1 1 1 2 1 3 1 4 1 15 1 16 1 17 1 18 1 19 1
4 0 1 1 3 1
5 0 2 1 0 1
6 0 3 1 1 1
7 0 0 1 2 1
0 0 5 1 7 1
1 0 6 1 4 1
2 0 7 1 5 1
3 0 4 1 6 1
1 1 1 5 1 0
0 1 0 5 0 0
0 4 1 0 0 2
1 4 0 0 1 2
0
1
# This Python script runs through all 3-manifold triangulations in this file # and prints the first homology of each. # # See the Regina handbook for more elaborate sample Python sessions.

# Output the homology of each triangulation. t = tri.firstChild() while t != None: print t.label() + ":", t.homology() t = t.nextSibling()