Izidor Hafner Mazes for Superintelligent Ginzburg projection
Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 2
Introduction
Let as take an example. We are given a uniform polyhedron.
10 4 small rhombidodecahedron 910, 4, ÅÅÅÅÅÅÅÅÅ , ÅÅÅÅÅ = 9 3
In Mathematica the polyhedron is given by a list of faces and with a list of koordinates of vertices [Roman E. Maeder, The Mathematica Programmer II, Academic Press1996]. The list of faces consists of a list of lists, where a face is represented by a list of vertices, which is given by a matrix. Let us show the first five faces:
81, 2, 6, 15, 26, 36, 31, 19, 10, 3< 81, 3, 9, 4< 81, 4, 11, 22, 29, 32, 30, 19, 13, 5< 81, 5, 8, 2< 82, 8, 17, 26, 38, 39, 37, 28, 16, 7<
The nest two figures represent faces and vertices. The polyhedron is projected onto supescribed sphere and the sphere is projected by a cartographic projection. Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 3 1
4 11 21 17 7
2 8 6 5 20 19 30 16 15 3
14 10 12 18 26 34 39 37 29 23
9 24 13 28 27 41 36 38 22 25
31 33 40 42 35
32
5 8 17 24 13
3 1 2 6 15 26 36 31 19 10
9 4 7 14 27 38 47 43 30 20 12 25 49 42 18 11 16 39 54 32 21 23 2837 50 57 53 44 29 22
3433 35 4048 56 60 59 52 41
45 51 58 55 46
The problem is to find the path from the black dot to gray dot, where thick lines represent walls of a maze. Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 4
The solution is given by a list of faces passed from the black to gray dot. 3
2
13 1 4 9
12 10
11 5 7 8
6 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 5 Problems Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 6
1.
5 5 5 small ditrigonal icosidodecahedron 9 ÅÅÅÅÅ , 3, ÅÅÅÅÅ , 3, ÅÅÅÅÅ , 3= 2 2 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 7
2.
5 small icosicosidodecahedron 96, ÅÅÅÅÅ , 6, 3= 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 8
3.
5 small snub icosicosidodecahedron 93, ÅÅÅÅÅ , 3, 3, 3, 3= 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 9
4.
3 small dodecicosidodecahedron 910, ÅÅÅÅÅ , 10, 5= 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 10
5.
5 5 5 5 5 small stellated dodecahedron 9 ÅÅÅÅÅ , ÅÅÅÅÅ , ÅÅÅÅÅ , ÅÅÅÅÅ , ÅÅÅÅÅ = 2 2 2 2 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 11
6.
1 great dodecahedron ÅÅÅÅÅ 85, 5, 5, 5, 5< 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 12
7.
5 5 dodecadodecahedron 9 ÅÅÅÅÅ , 5, ÅÅÅÅÅ , 5= 2 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 13
8.
5 truncated great dodecahedron 910, 10, ÅÅÅÅÅ = 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 14
9.
5 rhombidodecadodecahedron 94, ÅÅÅÅÅ , 4, 5= 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 15
10.
10 4 small rhombidodecahedron 910, 4, ÅÅÅÅÅÅÅÅÅ , ÅÅÅÅÅ = 9 3 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 16
11.
5 snub dodecadodecahedron 93, 3, ÅÅÅÅÅ , 3, 5= 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 17
12.
5 5 5 ditrigonal dodecadodecahedron 9 ÅÅÅÅÅ , 5, ÅÅÅÅÅ , 5, ÅÅÅÅÅ , 5= 3 3 3 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 18
13.
1 great icosahedron ÅÅÅÅÅ 83, 3, 3, 3, 3< 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 19
14.
5 5 great icosidodecahedron 9 ÅÅÅÅÅ , 3, ÅÅÅÅÅ , 3= 2 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 20
15.
5 great truncated icosahedron 96, 6, ÅÅÅÅÅ = 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 21
16.
6 4 rhombicosahedron 96, 4, ÅÅÅÅÅ , ÅÅÅÅÅ = 5 3 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 22
17.
5 great snub icosidodecahedron 93, 3, ÅÅÅÅÅ , 3, 3= 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 23
18.
pentagonal prism 84, 4, 5< Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 24
19.
pentagonal antiprism 83, 3, 3, 5< Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 25
20.
5 pentagrammic prism 94, 4, ÅÅÅÅÅ = 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 26
21.
5 pentagrammic antiprism 93, 3, 3, ÅÅÅÅÅ = 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 27
22.
5 pentagrammic crossed antiprism 93, 3, 3, ÅÅÅÅÅ = 3 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 28 Solutions Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 29
1.
5 5 5 small ditrigonal icosidodecahedron 9 ÅÅÅÅÅ , 3, ÅÅÅÅÅ , 3, ÅÅÅÅÅ , 3= 2 2 2
12
13 1 11
14 16 2 10 15 3
7 9 6 4 8
5 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 30
2.
5 small icosicosidodecahedron 96, ÅÅÅÅÅ , 6, 3= 2
21
16 20 221
19 17 15 18 14 2
12 4 11 13 3
9 7 5 10 8 6 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 31
3.
5 small snub icosicosidodecahedron 93, ÅÅÅÅÅ , 3, 3, 3, 3= 2
11 10
17 16 13 12 9 8 18 15 14 7
20 19 5 6 30
3 4 28 29 21 2 22 23 1 27
24 26
25 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 32
4.
3 small dodecicosidodecahedron 910, ÅÅÅÅÅ , 10, 5= 2
15
6 5 11 1013 14
7 4 3 129 18
2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 33
5.
5 5 5 5 5 small stellated dodecahedron 9 ÅÅÅÅÅ , ÅÅÅÅÅ , ÅÅÅÅÅ , ÅÅÅÅÅ , ÅÅÅÅÅ = 2 2 2 2 2
4
3 1 5 6 12
2 8 7 11 10
9 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 34
6.
1 great dodecahedron ÅÅÅÅÅ 85, 5, 5, 5, 5< 2
9
1 6 4 7 11
10 212 3 8
5 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 35
7.
5 5 dodecadodecahedron 9 ÅÅÅÅÅ , 5, ÅÅÅÅÅ , 5= 2 2
125
2110 14 15 2 13 116
198 20 9 163 1714 187 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 36
8.
5 truncated great dodecahedron 910, 10, ÅÅÅÅÅ = 2
10
8 12 3 6 4
111 2 7 13 149
5 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 37
9.
5 rhombidodecadodecahedron 94, ÅÅÅÅÅ , 4, 5= 2
5 202 18 16 148 126
1 3 19 17 15 13 7
4 10 21 9 11
22 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 38
10.
10 4 small rhombidodecahedron 910, 4, ÅÅÅÅÅÅÅÅÅ , ÅÅÅÅÅ = 9 3
12
9 13
11 8 10
7
4 6 2 5 1
3 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 39
11.
5 snub dodecadodecahedron 93, 3, ÅÅÅÅÅ , 3, 5= 2
24
15 23
2 12 14 2216 13 21 11 17 3 18 5 20 6 1 4 10 19
7 9
8 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 40
12.
5 5 5 ditrigonal dodecadodecahedron 9 ÅÅÅÅÅ , 5, ÅÅÅÅÅ , 5, ÅÅÅÅÅ , 5= 3 3 3
1217
14 23 2 1118 9 1316
145 203 1922 107 158
216 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 41
13.
1 great icosahedron ÅÅÅÅÅ 83, 3, 3, 3, 3< 2
14
10 18 8
12 6 16 3 5 20
19 1 7 11 2 17
4 13 15
9 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 42
14.
5 5 great icosidodecahedron 9 ÅÅÅÅÅ , 3, ÅÅÅÅÅ , 3= 2 2
4
9 1 13 7
18 8 14 5 3
15 17 10 2 12 6
11
16 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 43
15.
5 great truncated icosahedron 96, 6, ÅÅÅÅÅ = 2
5 8
3 13 11 14 15
7 94 6 10
1 12 2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 44
16.
6 4 rhombicosahedron 96, 4, ÅÅÅÅÅ , ÅÅÅÅÅ = 5 3
9 18 17 4 10
5 11
6 8 12 3 1 16 2
15 13 7
14 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 45
17.
5 great snub icosidodecahedron 93, 3, ÅÅÅÅÅ , 3, 3= 2
14
13 21 1 26 27 4 5 15 9 8 22 20 12 24 16 25 3 2 11 28 6 7 23 10 19 29 17 18 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 46
18.
pentagonal prism 84, 4, 5<
2
3 5 1
4 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 47
19.
pentagonal antiprism 83, 3, 3, 5<
7
8 6 2
1 5 3
4 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 48
20.
5 pentagrammic prism 94, 4, ÅÅÅÅÅ = 2
5
1 3 7 4 6
2 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 49
21.
5 pentagrammic antiprism 93, 3, 3, ÅÅÅÅÅ = 2
3
2 4 8
1 5 7
6 Cell[ TextData[ {"I. Hafner, Mazes for Superintelligent}], "Header"] 50
22.
5 pentagrammic crossed antiprism 93, 3, 3, ÅÅÅÅÅ = 3
3
8 2 4
1 7 5
6