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Updated 7 Sept 2002
Program Printouts
These printouts list the acceptable stellations of the icosahedron according to different conditions or rules.
Be warned, the listings may contain the odd error: the code has not been validated, and the printouts went through a dodgy OCR package to get them on the web, and had to be manually corrected.
The program itself was written in SAM BASIC and ran on a SAM Coupe with MasterDos. I will try and get the source code across, but don't hold your breath. (The algorithms are probably more interesting than the detailed code, unless you happen to be doubly-weird in working with both polyhedra and the SAM or an emulator).
Each printout gives: The conditions used, a note on their effect, the number of stellations found, and the actual list of acceptable stellations. The list gives each stellations' position number in the list, code number and modified DuVal symbol. These are explained below.
My program printout and dot matrix printer don't handle bold, italic or subscript very well. So for these purposes I have adopted a modified form of DuVal's notaton used in The fifty-nine icosahedra:
All symbols are in ordinary style (Courier) font. Dextro and laevo forms are identified by d and l suffixes, for example f1d and f1l .
Because a plain string of figures and numbers would be confusing, I separate the cell sets with commas.
The example above becomes D,e1,f1d,f2 .
I also allocate a code number to each stellation. This code number greatly simplifies the identification of stellations in my computer programs. For example to examine every combination of cells I can just do a "For n=1 to 4095" (where n is the code). This also has the virtue that the listings of stellations can be simply ordered by ascending codes.
The Du Val symbols and Code numbers are explained more fully in Towards stellating the icosahedron and faceting the icosahedron.
| The notations compared | ||||||||||||
| DuVal | a | b | c | d | e1 | e2 | f1 | f1 | f2 | g1 | g2 | h |
| Modified | a | b | c | d | e1 | e2 | f1d | f1l | f2 | g1 | g2 | h |
| Bit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| Code | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 | 2048 |
Stellations of the Icosahedron
3 conditions for acceptance:
No enantiomorphs
No hidden cavities
No separated shells
The 59 Icosahedra of Coxeter et al.
59 icosahedra found
No. Code DuVal Symbol
---- ---- ------------
1 l A
2 3 B
3 7 C
4 15 D
5 16 e1
6 31 D,el
7 32 e2
8 47 D,e2
9 63 E
10 64 f1d
11 80 el,fld
12 95 D,el,fld
13 96 e2,fld
14 11 D,e2,fld
15 127 E,fld
16 192 f1
17 208 el,fl
18 223 D,el,fl
19 255 E,fl
20 256 f2
21 288 e2,f2
22 303 D,e2,f2
23 319 E,f2
24 352 e2,fld,f2
25 367 D,e2,fld,f2
26 383 E,fld,f2
27 511 F
28 512 g1
29 576 fld,gl
30 592 el,fld,gl
31 607 D,el,fld,gl
32 608 e2,fld,gl
33 623 D,e2,fld,gl
34 639 E,fld,gl
35 704 fl,g1
36 720 el,fl,gl
37 735 D,el1fl,gl
36 767 E,fl,gl
39 864 e2,fld,f2,gl
40 879 D,e2,fld,f2,gl
41 895 E,fld,f2,gl
42 1023 F,gl
43 1024 g2
44 1088 fld,g2
45 1104 el,fld,g2
46 1119 D,el,fld,g2
47 1280 f2,g2
48 1312 e2,f2,g2
49 1327 D,e2,f2,g2
50 1343 E,f2,g2
51 1344 f1d,f2,g2
52 1360 e1,f1d,f2,g2
53 1375 D,e1,f1d,f2,g2
54 1376 e2,f1d,f2,g2
55 1391 D,e2,f1d,f2,g2
56 1407 E,f1d,f2,g2
57 1535 F,g2
58 2047 G
59 4095 H
Stellations of the Icosahedron
4 conditions for acceptance:
No enantiomorphs
No hidden cavities
No separated shells
Face planes continuous
Subset of 'The 59' with continuous faces.
34 icosahedra found
No. Code DuVal Symbol
---- ---- ------------
1 l A
2 3 B
3 7 C
4 15 D
5 31 D,el
6 47 D,e2
7 63 E
8 95 D,el,fld
9 111 D,e2,fld
10 127 E,fld
11 223 D,el,fl
12 255 E,fl
13 303 D,e2,f2
14 319 E,f2
15 367 D,e2,fld,f2
16 383 E,fld,f2
17 511 F
18 607 D,el,fld,gl
19 623 D,e2,fld,gl
20 639 E,fld,gl
21 735 D,el,fl,gl
22 767 E,fl,gl
23 879 D,e2,fld,f2,gl
24 895 E,fld,f2,gl
25 1023 F,gl
26 1119 D,el,fld,g2
27 1327 D,e2,f2,g2
28 1343 E,f2,g2
29 1375 D,el,fld,f2,g2
30 1391 D,e2,fld,f2,g2
31 1407 E,fld,f2,g2
32 1535 F,g2
33 2047 G
34 4095 H
Stellations of the Icosahedron
3 conditions for acceptance:
No enantiomorphs
No hidden cavities
Face planes continuous
Continuous faces in place of rule (v).
36 icosahedra found
No. Code DuVal Symbol
---- ---- ------------
1 l A
2 3 B
3 7 C
4 15 D
5 31 D,el
6 47 D,e2
7 63 E
8 95 D,el,fld
9 111 D,e2,fld
10 127 E,fld
11 223 D,e1,fl
12 255 E,f1
13 303 D,e2,f2
14 319 E,f2
15 351 D,e1,fld,f2
16 367 D,e2,fld,f2
17 383 E,fld,f2
18 511 F
19 607 D,e1,fld,gl
20 623 D,e2,f1d,g1
21 639 E,fld,gl
22 735 D,el,fl,gl
23 767 E,fl,gl
24 863 D,el,fld,f2,gl
25 879 D,e2,fld,f2,gl
26 895 E,fld,f2,gl
27 1023 F,gl
28 1119 D,el,fld,g2
29 1327 D,e2,f2,g2
30 1343 E,f2,g2
31 1375 D,el,fld,f2,g2
32 1391 D,e2,fld,f2,g2
33 1407 E,fld,f2,g2
34 1535 F,g2
35 2047 G
36 4095 H
Stellations of the Icosahedron
4 conditions for acceptance:
No enantiomorphs
No hidden cavities
No separated shells
No segmented edges
Subset of 'The 59' with continuous edges
25 icosahedra found
No. Code DuVal Symbol
---- ---- ------------
1 l A
2 3 B
3 7 C
4 15 D
5 31 D,el
6 47 D,e2
7 63 E
8 111 D,e2,fld
9 127 E,fld
10 223 D,el,fl
11 255 E,fl
12 303 D,e2,f2
13 319 E,f2
14 367 D,e2,fld,f2
15 383 E,fld,f2
16 511 F
17 623 D,e2,fld,gl
18 639 E,fld,g1
19 735 D,el,fl,gl
20 767 E,fl,gl
21 879 D,e2,fld,f2,gl
22 895 E,fld,f2,gl
23 1023 F,gl
24 2047 G
25 4095 H
Stellations of the Icosahedron
3 conditions for acceptance:
No enanti(omorphs
No hidden cavities
No segmented edges
Continuous edges in place of rule (v).
50 icosahedra found
No. Code DuVal Symbol
---- ---- ------------
1 l A
2 3 B
3 7 C
4 15 D
5 31 D,el
6 33 A,e2
7 35 B,e2
8 39 C,e2
9 47 D,e2
10 63 E
11 103 C,e2,fld
12 111 D,e2,fld
13 127 E,fld
14 223 D,el,f1
15 255 E,fl
16 289 A,e2,f2
17 291 B,e2,f2
18 295 C,e2,f2
19 303 D,e2,f2
20 319 E,f2
21 335 D,fld,f2
22 343 C,el,fld,f2
23 351 D,el,fld,f2
24 359 C,e2,fld,f2
25 367 D,e2,fld,f2
26 383 E,fld,f2
27 511 F
28 551 C,e2,gl
29 559 D,e2,gl
30 575 E,gl
31 615 C,e2,fld,gl
32 623 D,e2,fld,gl
33 639 E,fld,gl
34 735 D,el,fl,gl
35 767 E,fl,gl
36 783 D,f2,gl
37 791 C,el,f2,gl
38 799 D,el,f2,gl
39 807 C,e2,f2,gl
40 815 D,e2,f2,gl
41 831 E,f2,gl
42 847 D,fld,f2,gl
43 855 C,el,fld,f2,gl
44 863 D,el,fld,f2,gl
45 871 C,e2,fld,f2,gl
46 879 D,e2,fld,f2,gl
47 895 E,fld,f2,gl
48 1023 F,gl
49 2047 G
50 4095 H
Stellations of the Icosahedron
5 conditions for acceptance:
No enantiomorphs
No hidden cavities
No separated shells
No segmented edges
Face planes continuous
Subset of 'The 59' with continuous faces and edges.
25 icosahedra found
No. Code DuVal Symbol
---- ---- ------------
1 l A
2 3 B
3 7 C
4 15 D
5 31 D,el
6 47 D,e2
7 63 E
8 111 D,e2,fld
9 127 E,fld
10 223 D,el,fl
11 255 E,fl
12 303 D,e2,f2
13 319 E,f2
14 367 D,e2,fld,f2
15 383 E,fld,f2
16 511 F
17 623 D,e2,fld,gl
18 639 E,fld,gl
19 735 D,e1,fl,gl
20 767 E,fl,g1
21 879 D,e2,fld,f2,gl
22 895 E,fld,f2,gl
23 1023 F,gl
24 2047 G
25 4095 H
Stellations of the Icosahedron
4 conditions for acceptance:
No enantiomorphs
No hidden cavities
No segmented edges
Face planes continuous
Continuous faces and edges in place of rule (v).
27 icosahedra found
No. Code DuVal Symbol
---- ---- ------------
1 1 A
2 3 B
3 7 C
4 15 D
5 31 D,el
6 47 D,e2
7 63 E
8 111 D,e2,fld
9 127 E,f1d
10 223 D,el,fl
11 255 E,fl
12 303 D,e2,f2
13 319 E,f2
14 351 D,el,fld,f2
15 367 D,e2,fld,f2
16 383 E,fld,f2
17 511 F
18 623 D,e2,fld,gl
19 639 E,fld,gl
20 735 D,el,fl,gl
21 767 E,fl,gl
22 863 D,e1,f1d,f2,g1
23 879 D,e2,fld,f2,gl
24 895 E,fld,f2,gl
25 1023 F,gl
26 2047 G
27 4095 H
Top of page
Icosahedra Index
Other polyhedron sites
Email me
Updated 7 Sept 2002