List of geodesic polyhedra and Goldberg polyhedra#Octahedral
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This is a list of selected geodesic polyhedra and Goldberg polyhedra, two infinite classes of polyhedra. Geodesic polyhedra and Goldberg polyhedra are duals of each other. The geodesic and Goldberg polyhedra are parameterized by integers m and n, with and . T is the triangulation number, which is equal to .
Icosahedral
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| class="wikitable sortable sticky-header-multi" | |||||||||||||
| rowspan=2 | m
! rowspan=2 | n ! rowspan=2 | T ! rowspan=2 | Class ! rowspan=2 | Vertices ! rowspan=2 | Edges ! rowspan=2 | Faces ! rowspan=2 class="unsortable"|Face ! scope="col" colspan=3 class="unsortable"|Geodesic ! scope="col" colspan=3 class="unsortable"|Goldberg | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| class="unsortable"| Symbols
!class="unsortable"| Conway !class="unsortable"| Image !class="unsortable"| Symbols !class="unsortable"| Conway !class="unsortable"| Image | |||||||||||||
| 1 | 0 | 1 | I | 12 | 30 | 20 | 60px | {3,5} {3,5+}1,0 | I | 60px | {5,3} {5+,3}1,0 GP5(1,0) | D | 60px |
| 2 | 0 | 4 | I | 42 | 120 | 80 | 60px | {3,5+}2,0 | uI [https://levskaya.github.io/polyhedronisme/?recipe=A10dcdI dcdI] | 60px | {5+,3}2,0 GP5(2,0) | cD [https://levskaya.github.io/polyhedronisme/?recipe=A10cD cD] | 60px |
| 3 | 0 | 9 | I | 92 | 270 | 180 | 60px | {3,5+}3,0 | xI [https://levskaya.github.io/polyhedronisme/?recipe=A10ktI ktI] | 60px | {5+,3}3,0 GP5(3,0) | yD [https://levskaya.github.io/polyhedronisme/?recipe=A10tkD tkD] | 60px |
| 4 | 0 | 16 | I | 162 | 480 | 320 | 60px | {3,5+}4,0 | uuI [https://levskaya.github.io/polyhedronisme/?recipe=A100dccD dccD] | 60px | {5+,3}4,0 GP5(4,0) | [https://levskaya.github.io/polyhedronisme/?recipe=A100ccD c2D] | 60px |
| 5 | 0 | 25 | I | 252 | 750 | 500 | 60px | {3,5+}5,0 | u5I
[https://levskaya.github.io/polyhedronisme/?recipe=A20u5I u5I] | 60px | {5+,3}5,0 GP5(5,0) | c5D [https://levskaya.github.io/polyhedronisme/?recipe=A100du5I du5I] | 60px |
| 6 | 0 | 36 | I | 362 | 1080 | 720 | 60px | {3,5+}6,0 | uxI [https://levskaya.github.io/polyhedronisme/?recipe=A100dctkdI dctkdI] | 60px | {5+,3}6,0 GP5(6,0) | cyD [https://levskaya.github.io/polyhedronisme/?recipe=A100ctkD ctkD] | 60px |
| 7 | 0 | 49 | I | 492 | 1470 | 980 | 60px | {3,5+}7,0 | v{{overline|v}}I [https://levskaya.github.io/polyhedronisme/?recipe=A100dwrwdI dwrwdI] | 60px | {5+,3}7,0 GP5(7,0) | w{{overline|w}}D [https://levskaya.github.io/polyhedronisme/?recipe=A100wrwD wrwD] | 60px |
| 8 | 0 | 64 | I | 642 | 1920 | 1280 | 60px | {3,5+}8,0 | u3I [https://levskaya.github.io/polyhedronisme/?recipe=A100dcccdI dcccdI] | 60px | {5+,3}8,0 GP5(8,0) | [https://levskaya.github.io/polyhedronisme/?recipe=A100cccD cccD] | 60px |
| 9 | 0 | 81 | I | 812 | 2430 | 1620 | 60px | {3,5+}9,0 | xxI [https://levskaya.github.io/polyhedronisme/?recipe=A100ktktI ktktI] | 60px | {5+,3}9,0 GP5(9,0) | yyD [https://levskaya.github.io/polyhedronisme/?recipe=A100tktkD tktkD] | 60px |
| 10 | 0 | 100 | I | 1002 | 3000 | 2000 | 60px | {3,5+}10,0 | uu5I
[https://levskaya.github.io/polyhedronisme/?recipe=A20uu5I uu5I] |60px | {5+,3}10,0 GP5(10,0) | cc5D [https://levskaya.github.io/polyhedronisme/?recipe=A100cdu5I cdu5I] | 60px | |
| 11 | 0 | 121 | I | 1212 | 3630 | 2420 | 60px | {3,5+}11,0 | u11I
[https://levskaya.github.io/polyhedronisme/?recipe=A20u11I u11I] |60px | {5+,3}11,0 GP5(11,0) | c11D | ||
| 12 | 0 | 144 | I | 1442 | 4320 | 2880 | 60px | {3,5+}12,0 | uuxD [https://levskaya.github.io/polyhedronisme/?recipe=A100dcctkD dcctkD] | 60px | {5+,3}12,0 GP5(12,0) | ccyD [https://levskaya.github.io/polyhedronisme/?recipe=A100cctkD cctkD] | 60px |
| 13 | 0 | 169 | I | 1692 | 5070 | 3380 | 60px | {3,5+}13,0 | u13I
[https://levskaya.github.io/polyhedronisme/?recipe=A20u13I u13I] |60px | {5+,3}13,0 GP5(13,0) | c13D | ||
| 14 | 0 | 196 | I | 1962 | 5880 | 3920 | 60px | {3,5+}14,0 | uv{{overline|v}}I [https://levskaya.github.io/polyhedronisme/?recipe=A100dcwrwdI dcw{{overline|w}}dI] | 60px | {5+,3}14,0 GP5(14,0) | [https://levskaya.github.io/polyhedronisme/?recipe=A100cwrwD cwrwD] | 60px |
| 15 | 0 | 225 | I | 2252 | 6750 | 4500 | 60px | {3,5+}15,0 | u5xI [https://levskaya.github.io/polyhedronisme/?recipe=A20u5ktI u5ktI] | 60px | {5+,3}15,0 GP5(15,0) | c5yD c5tkD [https://levskaya.github.io/polyhedronisme/?recipe=A20du5ktI du5ktI] | 60px |
| 16 | 0 | 256 | I | 2562 | 7680 | 5120 | 60px | {3,5+}16,0 | [https://levskaya.github.io/polyhedronisme/?recipe=A100dccccD dc4dI] | 60px | {5+,3}16,0 GP5(16,0) | [https://levskaya.github.io/polyhedronisme/?recipe=A100ccccD ccccD] | 60px |
| 1 | 1 | 3 | II | 32 | 90 | 60 | 60px | {3,5+}1,1 | nI [https://levskaya.github.io/polyhedronisme/?recipe=A100kD kD] | 60px | {5+,3}1,1 GP5(1,1) | yD [https://levskaya.github.io/polyhedronisme/?recipe=A10tI tI] | 60px |
| 2 | 2 | 12 | II | 122 | 360 | 240 | 60px | {3,5+}2,2 | unI =dctI | 60px | {5+,3}2,2 GP5(2,2) | czD [https://levskaya.github.io/polyhedronisme/?recipe=A10cdkD cdkD] | 60px |
| 3 | 3 | 27 | II | 272 | 810 | 540 | 60px | {3,5+}3,3 | xnI [https://levskaya.github.io/polyhedronisme/?recipe=A100ktkD ktkD] | 60px | {5+,3}3,3 GP5(3,3) | yzD [https://levskaya.github.io/polyhedronisme/?recipe=A100tkdkD tkdkD] | 60px |
| 4 | 4 | 48 | II | 482 | 1440 | 960 | 60px | {3,5+}4,4 | u2nI [https://levskaya.github.io/polyhedronisme/?recipe=A100dcctI dcctI] | 60px | {5+,3}4,4 GP5(4,4) | c2zD [https://levskaya.github.io/polyhedronisme/?recipe=A100cctI cctI] | 60px |
| 5 | 5 | 75 | II | 752 | 2250 | 1500 | 60px | {3,5+}5,5 | u5nI | 60px | {5+,3}5,5 GP5(5,5) | c5zD | 60px |
| 6 | 6 | 108 | II | 1082 | 3240 | 2160 | 60px | {3,5+}6,6 | uxnI [https://levskaya.github.io/polyhedronisme/?recipe=A100dctktI dctktI] | 60px | {5+,3}6,6 GP5(6,6) | cyzD [https://levskaya.github.io/polyhedronisme/?recipe=A100ctkdkD ctkdkD] | 60px |
| 7 | 7 | 147 | II | 1472 | 4410 | 2940 | 60px | {3,5+}7,7 | v{{overline|v}}nI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwrwtI dwrwtI] | 60px | {5+,3}7,7 GP5(7,7) | w{{overline|w}}zD [https://levskaya.github.io/polyhedronisme/?recipe=A100wrwdkD wrwdkD] | 60px |
| 8 | 8 | 192 | II | 1922 | 5760 | 3840 | 60px | {3,5+}8,8 | u3nI [https://levskaya.github.io/polyhedronisme/?recipe=A100dccckD dccckD] | 60px | {5+,3}8,8 GP5(8,8) | c3zD [https://levskaya.github.io/polyhedronisme/?recipe=A100ccctI ccctI] | 60px |
| 9 | 9 | 243 | II | 2432 | 7290 | 4860 | 60px | {3,5+}9,9 | xxnI [https://levskaya.github.io/polyhedronisme/?recipe=A100ktktkD ktktkD] | 60px | {5+,3}9,9 GP5(9,9) | yyzD [https://levskaya.github.io/polyhedronisme/?recipe=A100tktktI tktktI] | 60px |
| 12 | 12 | 432 | II | 4322 | 12960 | 8640 | 60px | {3,5+}12,12 | uuxnI [https://levskaya.github.io/polyhedronisme/?recipe=A100dccdktkD dccdktkD] | 60px | {5+,3}12,12 GP5(12,12) | ccyzD [https://levskaya.github.io/polyhedronisme/?recipe=A100cckttI cckttI] | 60px |
| 14 | 14 | 588 | II | 5882 | 17640 | 11760 | 60px | {3,5+}14,14 | uv{{overline|v}}nI [https://levskaya.github.io/polyhedronisme/?recipe=A100dcwrwkD dcw{{overline|w}}kD] | 60px | {5+,3}14,14 GP5(14,14) | cw{{overline|w}}zD [https://levskaya.github.io/polyhedronisme/?recipe=A100cwrwtI cwrwtI] | 60px |
| 16 | 16 | 768 | II | 7682 | 23040 | 15360 | 60px | {3,5+}16,16 | uuuunI [https://levskaya.github.io/polyhedronisme/?recipe=A100dcccctI dcccctI] | 60px | {5+,3}16,16 GP5(16,16) | cccczD [https://levskaya.github.io/polyhedronisme/?recipe=A100cccctI cccctI] | 60px |
| 2 | 1 | 7 | III | 72 | 210 | 140 | 60px | {3,5+}2,1 | vI [https://levskaya.github.io/polyhedronisme/?recipe=A10dwD dwD] | 60px | {5+,3}2,1 GP5(2,1) | [https://levskaya.github.io/polyhedronisme/?recipe=A10wD wD] | 60px |
| 3 | 1 | 13 | III | 132 | 390 | 260 | 60px | {3,5+}3,1 | v3,1I | 60px | {5+,3}3,1 GP5(3,1) | w3,1D | 60px |
| 3 | 2 | 19 | III | 192 | 570 | 380 | 60px | {3,5+}3,2 | v3I | 60px | {5+,3}3,2 GP5(3,2) | w3D | 60px |
| 4 | 1 | 21 | III | 212 | 630 | 420 | 60px | {3,5+}4,1 | vnI |[https://levskaya.github.io/polyhedronisme/?recipe=A10dwtI dwtI] | 60px | {5+,3}4,1 GP5(4,1) | [https://levskaya.github.io/polyhedronisme/?recipe=A10wdkD wdkD] | 60px |
| 4 | 2 | 28 | III | 282 | 840 | 560 | 60px | {3,5+}4,2 | vnI [https://levskaya.github.io/polyhedronisme/?recipe=A10dtI dwtI] | 60px | {5+,3}4,2 GP5(4,2) | [https://levskaya.github.io/polyhedronisme/?recipe=A100wcD wcD] | 60px |
| 4 | 3 | 37 | III | 372 | 1110 | 740 | 60px | {3,5+}4,3 | v4I | {5+,3}4,3 GP5(4,3) | w4D | 60px | |
| 5 | 1 | 31 | III | 312 | 930 | 620 | 60px | {3,5+}5,1 | u5,1I | {5+,3}5,1 GP5(5,1) | w5,1D | 60px | |
| 5 | 2 | 39 | III | 392 | 1170 | 780 | 60px | {3,5+}5,2 | u5,2I | 60px | {5+,3}5,2 GP5(5,2) | w5,2D | 60px |
| 5 | 3 | 49 | III | 492 | 1470 | 980 | 60px | {3,5+}5,3 | vvI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwwD dwwD] | 60px | {5+,3}5,3 GP5(5,3) | [https://levskaya.github.io/polyhedronisme/?recipe=A100wwD wwD] | 60px |
| 6 | 2 | 52 | III | 522 | 1560 | 1040 | 60px | {3,5+}6,2 | v3,1uI | 60px | {5+,3}6,2 GP5(6,2) | w3,1cD | 60px |
| 6 | 3 | 63 | III | 632 | 1890 | 1260 | 60px | {3,5+}6,3 | vxI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwdktI dwdktI] | 60px | {5+,3}6,3 GP5(6,3) | wyD [https://levskaya.github.io/polyhedronisme/?recipe=A100wtkD wtkD] | 60px |
| 8 | 2 | 84 | III | 842 | 2520 | 1680 | 60px | {3,5+}8,2 | vunI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwctI dwctI] | {5+,3}8,2 GP5(8,2) | wczD [https://levskaya.github.io/polyhedronisme/?recipe=A100wcdkD wcdkD] | 60px | |
| 8 | 4 | 112 | III | 1122 | 3360 | 2240 | 60px | {3,5+}8,4 | vuuI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwccD dwccD] | {5+,3}8,4 GP5(8,4) | [https://levskaya.github.io/polyhedronisme/?recipe=A100wccD wccD] | 60px | |
| 11 | 2 | 147 | III | 1472 | 4410 | 2940 | 60px | {3,5+}11,2 | vvnI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwwtI dwwtI] | {5+,3}11,2 GP5(11,2) | [https://levskaya.github.io/polyhedronisme/?recipe=A100wwdkD wwzD] | 60px | |
| 12 | 3 | 189 | III | 1892 | 5670 | 3780 | 60px | {3,5+}12,3 | vxnI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwtktktI dwtktktI] | {5+,3}12,3 GP5(12,3) | wyzD [https://levskaya.github.io/polyhedronisme/?recipe=A100wtktI wtktI] | 60px | |
| 10 | 6 | 196 | III | 1962 | 5880 | 3920 | 60px | {3,5+}10,6 | vvuI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwwcD dwwcD] | {5+,3}10,6 GP5(10,6) | [https://levskaya.github.io/polyhedronisme/?recipe=A100wwcD wwcD] | 60px | |
| 12 | 6 | 252 | III | 2522 | 7560 | 5040 | 60px | {3,5+}12,6 | vxuI [https://levskaya.github.io/polyhedronisme/?recipe=A12dwctkD dwctkD] | {5+,3}12,6 GP5(12,6) | cywD [https://levskaya.github.io/polyhedronisme/?recipe=A100wctkD wctkD] | 60px | |
| 16 | 4 | 336 | III | 3362 | 10080 | 6720 | 60px | {3,5+}16,4 | vuunI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwcctI dwcctI] | {5+,3}16,4 GP5(16,4) | wcczD [https://levskaya.github.io/polyhedronisme/?recipe=A100wcctI wcctI] | 60px | |
| 14 | 7 | 343 | III | 3432 | 10290 | 6860 | 60px | {3,5+}14,7 | v{{overline|v}}vI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwrwwD dwrwwD] | {5+,3}14,7 GP5(14,7) | w{{overline|w}}wD [https://levskaya.github.io/polyhedronisme/?recipe=A100wrwwD wrwwD] | 60px | |
| 15 | 9 | 441 | III | 4412 | 13230 | 8820 | 60px | {3,5+}15,9 | vvxI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwwtkD dwwtkD] | {5+,3}15,9 GP5(15,9) | wwxD [https://levskaya.github.io/polyhedronisme/?recipe=A100wwtkD wwtkD] | 60px | |
| 16 | 8 | 448 | III | 4482 | 13440 | 8960 | 60px | {3,5+}16,8 | vuuuI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwcccD dwcccD] | {5+,3}16,8 GP5(16,8) | [https://levskaya.github.io/polyhedronisme/?recipe=A100wcccD wcccD] | 60px | |
| 18 | 1 | 343 | III | 3432 | 10290 | 6860 | {3,5+}18,1 | vvvI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwwwD dwwwD] | {5+,3}18,1 GP5(18,1) | [https://levskaya.github.io/polyhedronisme/?recipe=A100wwwD wwwD] | 60px | ||
| 18 | 9 | 567 | III | 5672 | 17010 | 11340 | {3,5+}18,9 | vxxI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwtktkD dwtktkD] | {5+,3}18,9 GP5(18,9) | wyyD [https://levskaya.github.io/polyhedronisme/?recipe=A100wtktkD wtktkD] | 60px | ||
| 20 | 12 | 784 | III | 7842 | 23520 | 15680 | {3,5+}20,12 | vvuuI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwwccD dwwccD] | {5+,3}20,12 GP5(20,12) | [https://levskaya.github.io/polyhedronisme/?recipe=A100wwccD wwccD] | 60px | ||
| 20 | 17 | 1029 | III | 10292 | 30870 | 20580 | {3,5+}20,17 | vvvnI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwwwtI dwwwtI] | {5+,3}20,17 GP5(20,17) | wwwzD [https://levskaya.github.io/polyhedronisme/?recipe=A100wwwdkD wwwdkD] | 60px | ||
| 28 | 7 | 1029 | III | 10292 | 30870 | 20580 | {3,5+}28,7 | v{{overline|v}}vnI [https://levskaya.github.io/polyhedronisme/?recipe=A100dwrwwdkD dwrwwdkD] | {5+,3}28,7 GP5(28,7) | w{{overline|w}}wzD [https://levskaya.github.io/polyhedronisme/?recipe=A100wrwwdkD wrwwdkD] | 60px |
Octahedral
| class="wikitable sortable sticky-header-multi" | |||||||||||||
| rowspan=2 | m
! rowspan=2 | n ! rowspan=2 | T ! rowspan=2 | Class ! rowspan=2 | Vertices ! rowspan=2 | Edges ! rowspan=2 | Faces ! rowspan=2 class="unsortable"|Face ! scope="col" colspan=3 class="unsortable"|Geodesic ! scope="col" colspan=3 class="unsortable"|Goldberg | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| class="unsortable"| Symbols
!class="unsortable"| Conway !class="unsortable"| Image !class="unsortable"| Symbols !class="unsortable"| Conway !class="unsortable"| Image | |||||||||||||
| 1 | 0 | 1 | I | 6 | 12 | 8 | 60px | {3,4} {3,4+}1,0 | O | 60px | {4,3} {4+,3}1,0 GP4(1,0) | |C | 60px |
| 2 | 0 | 4 | I | 18 | 48 | 32 | 60px | {3,4+}2,0 | dcC [https://levskaya.github.io/polyhedronisme/?recipe=A10dcC dcC] | 60px | {4+,3}2,0 GP4(2,0) | cC [https://levskaya.github.io/polyhedronisme/?recipe=A10cC cC] | 60px |
| 3 | 0 | 9 | I | 38 | 108 | 72 | 60px | {3,4+}3,0 | [https://levskaya.github.io/polyhedronisme/?recipe=A10ktO ktO] | 60px | {4+,3}3,0 GP4(3,0) | [https://levskaya.github.io/polyhedronisme/?recipe=A10tkC tkC] | 60px |
| 4 | 0 | 16 | I | 66 | 192 | 128 | 60px | {3,4+}4,0 | uuO [https://levskaya.github.io/polyhedronisme/?recipe=A10dccC dccC] | 60px | {4+,3}4,0 GP4(4,0) | [https://levskaya.github.io/polyhedronisme/?recipe=A10ccC ccC] | 60px |
| 5 | 0 | 25 | I | 102 | 300 | 200 | 60px | {3,4+}5,0 | u5O | 60px | {4+,3}5,0 GP4(5,0) | c5C | 60px |
| 6 | 0 | 36 | I | 146 | 432 | 288 | 60px | {3,4+}6,0 | uxO [https://levskaya.github.io/polyhedronisme/?recipe=A100dctkdO dctkdO] | 60px | {4+,3}6,0 GP4(6,0) | cyC [https://levskaya.github.io/polyhedronisme/?recipe=A2ctkC ctkC] | 60px |
| 7 | 0 | 49 | I | 198 | 588 | 392 | 60px | {3,4+}7,0 | [https://levskaya.github.io/polyhedronisme/?recipe=A10dwrwO dwrwO] | 60px | {4+,3}7,0 GP4(7,0) | [https://levskaya.github.io/polyhedronisme/?recipe=A10wrwO wrwO] | 60px |
| 8 | 0 | 64 | I | 258 | 768 | 512 | 60px | {3,4+}8,0 | uuuO [https://levskaya.github.io/polyhedronisme/?recipe=A10dcccC dcccC] | 60px | {4+,3}8,0 GP4(8,0) | [https://levskaya.github.io/polyhedronisme/?recipe=A10cccC cccC] | 60px |
| 9 | 0 | 81 | I | 326 | 972 | 648 | 60px | {3,4+}9,0 | xxO [https://levskaya.github.io/polyhedronisme/?recipe=A10ktktO ktktO] | 60px | {4+,3}9,0 GP4(9,0) | yyC [https://levskaya.github.io/polyhedronisme/?recipe=A10tktkC tktkC] | 60px |
| 1 | 1 | 3 | II | 14 | 36 | 24 | 60px | {3,4+}1,1 | kC | 60px | {4+,3}1,1 GP4(1,1) | tO | 60px |
| 2 | 2 | 12 | II | 50 | 144 | 96 | 60px | {3,4+}2,2 | ukC [https://levskaya.github.io/polyhedronisme/?recipe=A10dctO dctO] | {4+,3}2,2 GP4(2,2) | czC [https://levskaya.github.io/polyhedronisme/?recipe=A10ctO ctO] | 60px | |
| 3 | 3 | 27 | II | 110 | 324 | 216 | 60px | {3,4+}3,3 | [https://levskaya.github.io/polyhedronisme/?recipe=A10ktkC ktkC] | {4+,3}3,3 GP4(3,3) | [https://levskaya.github.io/polyhedronisme/?recipe=A10tktO tktO] | 60px | |
| 4 | 4 | 48 | II | 194 | 576 | 384 | 60px | {3,4+}4,4 | uunO [https://levskaya.github.io/polyhedronisme/?recipe=A10dcctO dcctO] | {4+,3}4,4 GP4(4,4) | cczC [https://levskaya.github.io/polyhedronisme/?recipe=A10cctO cctO] | 60px | |
| 2 | 1 | 7 | III | 30 | 84 | 56 | 60px | {3,4+}2,1 | vO [https://levskaya.github.io/polyhedronisme/?recipe=A10dwC dwC] | 60px | {4+,3}2,1 GP4(2,1) | [https://levskaya.github.io/polyhedronisme/?recipe=A10wC wC] | 60px |
Tetrahedral
| class="wikitable sortable sticky-header-multi" | |||||||||||||
| rowspan=2 | m
! rowspan=2 | n ! rowspan=2 | T ! rowspan=2 | Class ! rowspan=2 | Vertices ! rowspan=2 | Edges ! rowspan=2 | Faces ! rowspan=2 class="unsortable"|Face ! scope="col" colspan=3 class="unsortable"|Geodesic ! scope="col" colspan=3 class="unsortable"|Goldberg | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| class="unsortable"| Symbols
!class="unsortable"| Conway !class="unsortable"| Image !class="unsortable"| Symbols !class="unsortable"| Conway !class="unsortable"| Image | |||||||||||||
| 1 | 0 | 1 | I | 4 | 6 | 4 | 60px | {3,3} {3,3+}1,0 | T | 60px | {3,3} {3+,3}1,0 GP3(1,0) | T | 60px |
| |1 | 1 | 3 | II | 8 | 18 | 12 | 60px | {3,3+}1,1 | kT [https://levskaya.github.io/polyhedronisme/?recipe=C100kT kT] | 60px | {3+,3}1,1 GP3(1,1) | tT [https://levskaya.github.io/polyhedronisme/?recipe=C100tT tT] | 60px |
| 2 | 0 | 4 | I | 10 | 24 | 16 | 60px | {3,3+}2,0 | dcT [https://levskaya.github.io/polyhedronisme/?recipe=C100dcT dcT] | 60px | {3+,3}2,0 GP3(2,0) | cT [https://levskaya.github.io/polyhedronisme/?recipe=C100cT cT] | 60px |
| 3 | 0 | 9 | I | 20 | 54 | 36 | 60px | {3,3+}3,0 | [https://levskaya.github.io/polyhedronisme/?recipe=C100ktT ktT] | 60px | {3+,3}3,0 GP3(3,0) | [https://levskaya.github.io/polyhedronisme/?recipe=C100tkT tkT] | 60px |
| 4 | 0 | 16 | I | 34 | 96 | 64 | 60px | {3,3+}4,0 | uuT [https://levskaya.github.io/polyhedronisme/?recipe=C100dccT dccT] | 60px | {3+,3}4,0 GP3(4,0) | [https://levskaya.github.io/polyhedronisme/?recipe=C100ccT ccT] | 60px |
| 5 | 0 | 25 | I | 52 | 150 | 100 | 60px | {3,3+}5,0 | u5T | 60px | {3+,3}5,0 GP3(5,0) | c5T | 60px |
| 6 | 0 | 36 | I | 74 | 216 | 144 | 60px | {3,3+}6,0 | uxT [https://levskaya.github.io/polyhedronisme/?recipe=A100dctkdT dctkdT] | 60px | {3+,3}6,0 GP3(6,0) | cyT [https://levskaya.github.io/polyhedronisme/?recipe=A100ctkD ctkT] | 60px |
| 7 | 0 | 49 | I | 100 | 294 | 196 | 60px | {3,3+}7,0 | vrvT [https://levskaya.github.io/polyhedronisme/?recipe=C100dwrwT dwrwT] | 60px | {3+,3}7,0 GP3(7,0) | [https://levskaya.github.io/polyhedronisme/?recipe=C100wrwT wrwT] | 60px |
| 8 | 0 | 64 | I | 130 | 384 | 256 | 60px | {3,3+}8,0 | u3T [https://levskaya.github.io/polyhedronisme/?recipe=A100dcccdT dcccdT] | 60px | {3+,3}8,0 GP3(8,0) | c3T [https://levskaya.github.io/polyhedronisme/?recipe=A100cccD cccT] | 60px |
| 9 | 0 | 81 | I | 164 | 486 | 324 | 60px | {3,3+}9,0 | xxT [https://levskaya.github.io/polyhedronisme/?recipe=C100ktktT ktktT] | 60px | {3+,3}9,0 GP3(9,0) | yyT [https://levskaya.github.io/polyhedronisme/?recipe=C100tktkT tktkT] | 60px |
| 3 | 3 | 27 | II | 56 | 162 | 108 | 60px | {3,3+}3,3 | [https://levskaya.github.io/polyhedronisme/?recipe=C100ktkT ktkT] | {3+,3}3,3 GP3(3,3) | [https://levskaya.github.io/polyhedronisme/?recipe=C100tktT tktT] | 60px | |
| 2 | 1 | 7 | III | 16 | 42 | 28 | 60px | {3,3+}2,1 | [https://levskaya.github.io/polyhedronisme/?recipe=C100dwT dwT] | 60px | {3+,3}2,1 GP5(2,1) | [https://levskaya.github.io/polyhedronisme/?recipe=C100wT wT] | 60px |
References
- {{Citation|last1=Wenninger |first1=Magnus |author1-link=Magnus Wenninger |title=Spherical Models |publisher=Cambridge University Press |isbn=978-0-521-29432-4 |mr=552023 |year=1979 |url=https://digitalcommons.csbsju.edu/saint_johns_abbey_books/82/ |url-status=live |archiveurl=https://web.archive.org/web/20080704103400/http://www.employees.csbsju.edu/mwenninger/magnus2000.html |archivedate=July 4, 2008}} Reprinted by Dover 1999 {{ISBN|978-0-486-40921-4}}
{{DEFAULTSORT:Geodesic polyhedra and Goldberg polyhedra}}