Let us define the following symbols to refer to types of geometric and topological relatedness:
≅ - standard geometric congruence, by any of {rotation, translation, reflection}~ - standard geometric similarilty, by any of {scaling, rotation, translation, reflection} - geometric congruence following reflection and any of {scaling, rotation, translation, and topological stretching} - geometric congruence following rotation and any of {scaling, translation, and topological stretching} (but not reflection)
0,3
1
2
f
0
1
2 1
3 0
1
0
1
2
3
4
5
6
10
11
12
13
14
15
16
11
1
2
3
4
5
6
0 7
111
112
113
114
115
116
117
110
12
1
2
3
4
121
122
123
124
136
13
5
6
7
8
9
1
2
3
4
0
131
132
133
134
135
137
130
138
139
145
146
147
140
14
7
8
9
6
1
2
3
4
5
0
141
142
143
144
148
149
15
5
7
8
6
1
2
3
4
0
151
152
153
154
155
156
157
150
158
1
2
3
4
5
6
7
8
9
139
150
117
140
149