Esta es una lista de poliedros geodésicos seleccionados y poliedros de Goldberg , dos clases infinitas de poliedros . Los poliedros geodésicos y los poliedros de Goldberg son duales entre sí. El geodésica y poliedros Goldberg se parametrizan por números enteros m y n , con y . T es el número de triangulación, que es igual a.
Icosaédrico
metro | norte | T | Clase | Vértices (geodésicos) Caras (Goldberg) | Bordes | Caras (geodésicas) Vértices (Goldberg) | Triángulo de la cara | Geodésico | Goldberg | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Simbolos | Conway | Imagen | Simbolos | Conway | Imagen | ||||||||
1 | 0 | 1 | I | 12 | 30 | 20 | ![]() | {3,5} {3,5+} 1,0 | I | ![]() | {5,3} {5 +, 3} 1,0 GP 5 (1,0) | D | ![]() |
2 | 0 | 4 | I | 42 | 120 | 80 | ![]() | {3,5+} 2,0 | uI dcdI | ![]() | {5 +, 3} 2,0 GP 5 (2,0) | CD CD | ![]() |
3 | 0 | 9 | I | 92 | 270 | 180 | ![]() | {3,5+} 3,0 | xI ktI | ![]() | {5 +, 3} 3,0 GP 5 (3,0) | yD tkD | ![]() |
4 | 0 | dieciséis | I | 162 | 480 | 320 | ![]() | {3,5+} 4,0 | uuI dccD | ![]() | {5 +, 3} 4,0 GP 5 (4,0) | c 2 D | ![]() |
5 | 0 | 25 | I | 252 | 750 | 500 | ![]() | {3,5+} 5,0 | u5I | ![]() | {5 +, 3} 5,0 GP 5 (5,0) | c5D | ![]() |
6 | 0 | 36 | I | 362 | 1080 | 720 | ![]() | {3,5+} 6,0 | ux I dctkdI | ![]() | {5 +, 3} 6,0 GP 5 (6,0) | cyD ctkD | ![]() |
7 | 0 | 49 | I | 492 | 1470 | 980 | ![]() | {3,5+} 7,0 | v v I dwrwdI | ![]() | {5 +, 3} 7,0 GP 5 (7,0) | w w D wrwD | ![]() |
8 | 0 | 64 | I | 642 | 1920 | 1280 | ![]() | {3,5+} 8,0 | u 3 yo dcccdI | ![]() | {5 +, 3} 8,0 GP 5 (8,0) | cccD | ![]() |
9 | 0 | 81 | I | 812 | 2430 | 1620 | ![]() | {3,5+} 9,0 | xxI ktktI | ![]() | {5 +, 3} 9,0 GP 5 (9,0) | yyD tktkD | ![]() |
10 | 0 | 100 | I | 1002 | 3000 | 2000 | ![]() | {3,5+} 10,0 | uu5I | ![]() | {5 +, 3} 10,0 GP 5 (10,0) | cc5D | ![]() |
11 | 0 | 121 | I | 1212 | 3630 | 2420 | ![]() | {3,5+} 11,0 | u11I | ![]() | {5 +, 3} 11,0 GP 5 (11,0) | c11D | |
12 | 0 | 144 | I | 1442 | 4320 | 2880 | ![]() | {3,5+} 12,0 | uuxD dcctkD | ![]() | {5 +, 3} 12,0 GP 5 (12,0) | ccyD cctkD | ![]() |
13 | 0 | 169 | I | 1692 | 5070 | 3380 | ![]() | {3,5+} 13,0 | u13I | ![]() | {5 +, 3} 13,0 GP 5 (13,0) | c13D | |
14 | 0 | 196 | I | 1962 | 5880 | 3920 | ![]() | {3,5+} 14,0 | uv v I dcw w dI | ![]() | {5 +, 3} 14,0 GP 5 (14,0) | cwrwD | ![]() |
15 | 0 | 225 | I | 2252 | 6750 | 4500 | ![]() | {3,5+} 15,0 | u5xI u5ktI | ![]() | {5 +, 3} 15,0 GP 5 (15,0) | c5yD c5tkD | ![]() |
dieciséis | 0 | 256 | I | 2562 | 7680 | 5120 | ![]() | {3,5+} 16,0 | dc 4 dI | ![]() | {5 +, 3} 16,0 GP 5 (16,0) | ccccD | ![]() |
1 | 1 | 3 | II | 32 | 90 | 60 | ![]() | {3,5+} 1,1 | nI kD | ![]() | {5 +, 3} 1,1 GP 5 (1,1) | yD ktD | ![]() |
2 | 2 | 12 | II | 122 | 360 | 240 | ![]() | {3,5+} 2,2 | unI = dctI | ![]() | {5 +, 3} 2,2 GP 5 (2,2) | czD cdkD | ![]() |
3 | 3 | 27 | II | 272 | 810 | 540 | ![]() | {3,5+} 3,3 | xnI ktkD | ![]() | {5 +, 3} 3,3 GP 5 (3,3) | yzD tkdkD | ![]() |
4 | 4 | 48 | II | 482 | 1440 | 960 | ![]() | {3,5+} 4,4 | u 2 n I dcctI | ![]() | {5 +, 3} 4,4 GP 5 (4,4) | c 2 zD cctI | ![]() |
5 | 5 | 75 | II | 752 | 2250 | 1500 | ![]() | {3,5+} 5,5 | u5nI | ![]() | {5 +, 3} 5,5 GP 5 (5,5) | c5zD | ![]() |
6 | 6 | 108 | II | 1082 | 3240 | 2160 | ![]() | {3,5+} 6,6 | uxnI dctktI | ![]() | {5 +, 3} 6,6 GP 5 (6,6) | cyz D ctkdkD | ![]() |
7 | 7 | 147 | II | 1472 | 4410 | 2940 | ![]() | {3,5+} 7,7 | v v nI dwrwtI | ![]() | {5 +, 3} 7,7 GP 5 (7,7) | w w z D wrwdkD | ![]() |
8 | 8 | 192 | II | 1922 | 5760 | 3840 | ![]() | {3,5+} 8,8 | T 3 nI dccckD | ![]() | {5 +, 3} 8,8 GP 5 (8,8) | c 3 z D ccctI | ![]() |
9 | 9 | 243 | II | 2432 | 7290 | 4860 | ![]() | {3,5+} 9,9 | xxnI ktktkD | ![]() | {5 +, 3} 9,9 GP 5 (9,9) | yyzD tktktI | ![]() |
12 | 12 | 432 | II | 4322 | 12960 | 8640 | ![]() | {3,5+} 12,12 | uuxnI dccdktkD | ![]() | {5 +, 3} 12,12 GP 5 (12,12) | ccyzD cckttI | ![]() |
14 | 14 | 588 | II | 5882 | 17640 | 11760 | ![]() | {3,5+} 14,14 | uv v nI DCW w kD | ![]() | {5 +, 3} 14,14 GP 5 (14,14) | cw w zD cwrwtI | ![]() |
dieciséis | dieciséis | 768 | II | 7682 | 23040 | 15360 | ![]() | {3,5+} 16,16 | uuuunI dcccctI | ![]() | {5 +, 3} 16,16 GP 5 (16,16) | cccczD cccctI | ![]() |
2 | 1 | 7 | III | 72 | 210 | 140 | ![]() | {3,5+} 2,1 | vI dwD | ![]() | {5 +, 3} 2,1 GP 5 (2,1) | wD | ![]() |
3 | 1 | 13 | III | 132 | 390 | 260 | ![]() | {3,5+} 3,1 | v3,1I | ![]() | {5 +, 3} 3,1 GP 5 (3,1) | w3,1D | ![]() |
3 | 2 | 19 | III | 192 | 570 | 380 | ![]() | {3,5+} 3,2 | v3I | ![]() | {5 +, 3} 3,2 GP 5 (3,2) | w3D | ![]() |
4 | 1 | 21 | III | 212 | 630 | 420 | ![]() | {3,5+} 4,1 | dwtI | ![]() | {5 +, 3} 4,1 GP 5 (4,1) | semana | ![]() |
4 | 2 | 28 | III | 282 | 840 | 560 | ![]() | {3,5+} 4,2 | vnI dwtI | ![]() | {5 +, 3} 4,2 GP 5 (4,2) | wdkD | ![]() |
4 | 3 | 37 | III | 372 | 1110 | 740 | ![]() | {3,5+} 4,3 | v4I | {5 +, 3} 4,3 GP 5 (4,3) | w4D | ![]() | |
5 | 1 | 31 | III | 312 | 930 | 620 | ![]() | {3,5+} 5,1 | u5,1I | {5 +, 3} 5,1 GP 5 (5,1) | w5,1D | ![]() | |
5 | 2 | 39 | III | 392 | 1170 | 780 | ![]() | {3,5+} 5,2 | u5,2I | ![]() | {5 +, 3} 5,2 GP 5 (5,2) | w5,2D | ![]() |
5 | 3 | 49 | III | 492 | 1470 | 980 | ![]() | {3,5+} 5,3 | vvI dwwD | ![]() | {5 +, 3} 5,3 GP 5 (5,3) | wwD | ![]() |
6 | 2 | 52 | III | 522 | 1560 | 1040 | ![]() | {3,5+} 6,2 | v3,1uI | ![]() | {5 +, 3} 6,2 GP 5 (6,2) | w3,1cD | ![]() |
6 | 3 | 63 | III | 632 | 1890 | 1260 | ![]() | {3,5+} 6,3 | vxI dwdktI | ![]() | {5 +, 3} 6,3 GP 5 (6,3) | wyD wtkD | ![]() |
8 | 2 | 84 | III | 842 | 2520 | 1680 | ![]() | {3,5+} 8,2 | vunI dwctI | {5 +, 3} 8,2 GP 5 (8,2) | wczD wcdkD | ![]() | |
8 | 4 | 112 | III | 1122 | 3360 | 2240 | ![]() | {3,5+} 8,4 | vuuI dwccD | {5 +, 3} 8,4 GP 5 (8,4) | wccD | ![]() | |
11 | 2 | 147 | III | 1472 | 4410 | 2940 | ![]() | {3,5+} 11,2 | vvnI dwwtI | {5 +, 3} 11,2 GP 5 (11,2) | wwzD | ![]() | |
12 | 3 | 189 | III | 1892 | 5670 | 3780 | ![]() | {3,5+} 12,3 | vxnI dwtktktI | {5 +, 3} 12,3 GP 5 (12,3) | wyzD wtktI | ![]() | |
10 | 6 | 196 | III | 1962 | 5880 | 3920 | ![]() | {3,5+} 10,6 | vvuI dwwcD | {5 +, 3} 10,6 GP 5 (10,6) | wwcD | ![]() | |
12 | 6 | 252 | III | 2522 | 7560 | 5040 | ![]() | {3,5+} 12,6 | vxuI dwdktcI | {5 +, 3} 12,6 GP 5 (12,6) | cywD wctkD | ![]() | |
dieciséis | 4 | 336 | III | 3362 | 10080 | 6720 | ![]() | {3,5+} 16,4 | vuunI dwdckD | {5 +, 3} 16,4 GP 5 (16,4) | wcczD wcctI | ![]() | |
14 | 7 | 343 | III | 3432 | 10290 | 6860 | ![]() | {3,5+} 14,7 | v v vI dwrwwD | {5 +, 3} 14,7 GP 5 (14,7) | w w wD wrwwD | ![]() | |
15 | 9 | 441 | III | 4412 | 13230 | 8820 | ![]() | {3,5+} 15,9 | vvxI dwwtkD | {5 +, 3} 15,9 GP 5 (15,9) | wwxD wwtkD | ![]() | |
dieciséis | 8 | 448 | III | 4482 | 13440 | 8960 | ![]() | {3,5+} 16,8 | vuuuI dwcccD | {5 +, 3} 16,8 GP 5 (16,8) | wcccD | ![]() | |
18 | 1 | 343 | III | 3432 | 10290 | 6860 | {3,5+} 18,1 | vvvI dwwwD | {5 +, 3} 18,1 GP 5 (18,1) | wwwD | ![]() | ||
18 | 9 | 567 | III | 5672 | 17010 | 11340 | {3,5+} 18,9 | vxxI dwtktkD | {5 +, 3} 18,9 GP 5 (18,9) | wyyD wtktkD | ![]() | ||
20 | 12 | 784 | III | 7842 | 23520 | 15680 | {3,5+} 20,12 | vvuuI dwwccD | {5 +, 3} 20,12 GP 5 (20,12) | wwccD | ![]() | ||
20 | 17 | 1029 | III | 10292 | 30870 | 20580 | {3,5+} 20,17 | vvvnI dwwwtI | {5 +, 3} 20,17 GP 5 (20,17) | wwwzD wwwdkD | ![]() | ||
28 | 7 | 1029 | III | 10292 | 30870 | 20580 | {3,5+} 28,7 | v v vnI dwrwwdkD | {5 +, 3} 28,7 GP 5 (28,7) | w w wzD wrwwdkD | ![]() |
Octaédrico
metro | norte | T | Clase | Vértices (geodésicos) Caras (Goldberg) | Bordes | Caras (geodésicas) Vértices (Goldberg) | Triángulo de la cara | Geodésico | Goldberg | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Simbolos | Conway | Imagen | Simbolos | Conway | Imagen | ||||||||
1 | 0 | 1 | I | 6 | 12 | 8 | ![]() | {3,4} {3,4+} 1,0 | O | ![]() | {4,3} {4 +, 3} 1,0 GP 4 (1,0) | C | ![]() |
2 | 0 | 4 | I | 18 | 48 | 32 | ![]() | {3,4+} 2,0 | dcC dcC | ![]() | {4 +, 3} 2,0 GP 4 (2,0) | cC cC | ![]() |
3 | 0 | 9 | I | 38 | 108 | 72 | ![]() | {3,4+} 3,0 | ktO | ![]() | {4 +, 3} 3,0 GP 4 (3,0) | tkC | ![]() |
4 | 0 | dieciséis | I | 66 | 192 | 128 | ![]() | {3,4+} 4,0 | uuO dccC | ![]() | {4 +, 3} 4,0 GP 4 (4,0) | ccC | ![]() |
5 | 0 | 25 | I | 102 | 300 | 200 | ![]() | {3,4+} 5,0 | u5O | ![]() | {4 +, 3} 5,0 GP 4 (5,0) | c5C | ![]() |
6 | 0 | 36 | I | 146 | 432 | 288 | ![]() | {3,4+} 6,0 | uxO dctkdO | ![]() | {4 +, 3} 6,0 GP 4 (6,0) | cyC ctkC | ![]() |
7 | 0 | 49 | I | 198 | 588 | 392 | ![]() | {3,4+} 7,0 | dwrwO | ![]() | {4 +, 3} 7,0 GP 4 (7,0) | wrwO | ![]() |
8 | 0 | 64 | I | 258 | 768 | 512 | ![]() | {3,4+} 8,0 | uuuO dcccC | ![]() | {4 +, 3} 8,0 GP 4 (8,0) | cccC | ![]() |
9 | 0 | 81 | I | 326 | 972 | 648 | ![]() | {3,4+} 9,0 | xxO ktktO | ![]() | {4 +, 3} 9,0 GP 4 (9,0) | yyC tktkC | ![]() |
1 | 1 | 3 | II | 14 | 36 | 24 | ![]() | {3,4+} 1,1 | kC | {4 +, 3} 1,1 GP 4 (1,1) | a | ![]() | |
2 | 2 | 12 | II | 50 | 144 | 96 | ![]() | {3,4+} 2,2 | ukC dctO | {4 +, 3} 2,2 GP 4 (2,2) | czC ctO | ![]() | |
3 | 3 | 27 | II | 110 | 324 | 216 | ![]() | {3,4+} 3,3 | ktkC | {4 +, 3} 3,3 GP 4 (3,3) | tktO | ![]() | |
4 | 4 | 48 | II | 194 | 576 | 384 | ![]() | {3,4+} 4,4 | uunO dcctO | {4 +, 3} 4,4 GP 4 (4,4) | cczC cctO | ![]() | |
2 | 1 | 7 | III | 30 | 84 | 56 | ![]() | {3,4+} 2,1 | vO dwC | ![]() | {4 +, 3} 2,1 GP 4 (2,1) | WC | ![]() |
Tetraédrico
metro | norte | T | Clase | Vértices (geodésicos) Caras (Goldberg) | Bordes | Caras (geodésicas) Vértices (Goldberg) | Triángulo de la cara | Geodésico | Goldberg | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Simbolos | Conway | Imagen | Simbolos | Conway | Imagen | ||||||||
1 | 0 | 1 | I | 4 | 6 | 4 | ![]() | {3,3} {3,3+} 1,0 | T | ![]() | {3,3} {3 +, 3} 1,0 GP 3 (1,0) | T | ![]() |
1 | 1 | 3 | II | 8 | 18 | 12 | ![]() | {3,3+} 1,1 | kT kT | {3 +, 3} 1,1 GP 3 (1,1) | tT tT | ![]() | |
2 | 0 | 4 | I | 10 | 24 | dieciséis | ![]() | {3,3+} 2,0 | dcT dcT | ![]() | {3 +, 3} 2,0 GP 3 (2,0) | cT cT | ![]() |
3 | 0 | 9 | I | 20 | 54 | 36 | ![]() | {3,3+} 3,0 | ktT | ![]() | {3 +, 3} 3,0 GP 3 (3,0) | tkT | ![]() |
4 | 0 | dieciséis | I | 34 | 96 | 64 | ![]() | {3,3+} 4,0 | uuT dccT | ![]() | {3 +, 3} 4,0 GP 3 (4,0) | ccT | ![]() |
5 | 0 | 25 | I | 52 | 150 | 100 | ![]() | {3,3+} 5,0 | u5T | ![]() | {3 +, 3} 5,0 GP 3 (5,0) | c5T | ![]() |
6 | 0 | 36 | I | 74 | 216 | 144 | ![]() | {3,3+} 6,0 | uxT dctkdT | ![]() | {3 +, 3} 6,0 GP 3 (6,0) | cyT ctkT | ![]() |
7 | 0 | 49 | I | 100 | 294 | 196 | ![]() | {3,3+} 7,0 | vrvT dwrwT | ![]() | {3 +, 3} 7,0 GP 3 (7,0) | wrwT | ![]() |
8 | 0 | 64 | I | 130 | 384 | 256 | ![]() | {3,3+} 8,0 | u 3 T dcccdT | ![]() | {3 +, 3} 8,0 GP 3 (8,0) | c 3 T cccT | ![]() |
9 | 0 | 81 | I | 164 | 486 | 324 | ![]() | {3,3+} 9,0 | xxT ktktT | ![]() | {3 +, 3} 9,0 GP 3 (9,0) | yyT tktkT | ![]() |
3 | 3 | 27 | II | 56 | 162 | 108 | ![]() | {3,3+} 3,3 | ktkT | {3 +, 3} 3,3 GP 3 (3,3) | tktT | ![]() | |
2 | 1 | 7 | III | dieciséis | 42 | 28 | ![]() | {3,3+} 2,1 | dwT | ![]() | {3 +, 3} 2,1 GP 5 (2,1) | wT | ![]() |
Referencias
- Wenninger, Magnus (1979), modelos esféricos , Cambridge University Press, ISBN 978-0-521-29432-4, MR 0552023 , archivado desde el original el 4 de julio de 2008 Reimpreso por Dover 1999 ISBN 978-0-486-40921-4