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Ĉi tiu tabelo enhavas indeksitan liston de la uniformaj kaj steligitaj pluredroj de la libro Pluredraj Modeloj de Magnus Wenninger.
La libro estis skribita kiel gvidilo por konstrui pluredrojn kiel fizikaj modeloj. Ĝi inkluzivas ŝablonojn de la edroj por konstruado, kaj ankaŭ mallonge priskribas la teorion malantaŭ de ĉi tiuj formoj.
Ĝi enhavas la 75 neprismajn uniformajn pluredrojn, kaj ankaŭ 44 steligitajn formojn de konveksaj regulaj pluredroj.
Specoj de pluredrojlistigita ĉi tie povas esti referencitaj kiel "Modelo de Wenninger numero N", aŭ WN.
La pluredroj estas grupitaj pli sube en 5 tabelojn: regula (1 ... 5), duonregula (6 ... 18), regulaj stelaj pluredroj (20 ... 22, 41), steligoj kaj kombinaĵoj (19 ... 66), kaj uniformaj stelaj pluredroj (67 ... 119). La kvar regulaj stelaj pluredroj estas listitaj dufoje ĉar ili apartenan kaj al uniformaj pluredroj kaj al stelaj.
[redaktu] Platonaj solidoj (regulaj) W1 ... W5
Indekso |
Nomo |
Bildo |
Simbolo de Wythoff |
Vertica figuro
kaj Simbolo de Schläfli |
Geometria simetria grupo |
U# |
K# |
V |
E |
F |
Edroj laŭ speco |
1 |
Kvaredro |
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3|2 3 |
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{3,3} |
Td |
U01 |
K06 |
4 |
6 |
4 |
4{3} |
2 |
Okedro |
 |
4|2 3 |
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{3,4} |
Oh |
U05 |
K10 |
6 |
12 |
8 |
8{3} |
3 |
Sesedro (Kubo) |
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3|2 4 |
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{4,3} |
Oh |
U06 |
K11 |
8 |
12 |
6 |
6{4} |
4 |
Dudekedro |
 |
5|2 3 |
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{3,5} |
Ih |
U22 |
K27 |
12 |
30 |
20 |
20{3} |
5 |
Dekduedro |
 |
3|2 5 |
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{5,3} |
Ih |
U23 |
K28 |
20 |
30 |
12 |
12{5} |
[redaktu] Arĥimedaj solidoj (duonregulaj) W6 ... W18
Indekso |
Nomo |
Bildo |
Simbolo de Wythoff |
Vertica figuro |
Geometria simetria grupo |
U# |
K# |
V |
E |
F |
Edroj laŭ speco |
6 |
Senpintigita kvaredro |
 |
2 3|3 |
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3.6.6 |
Td |
U02 |
K07 |
12 |
18 |
8 |
4{3}+4{6} |
7 |
Senpintigita okedro |
 |
2 4|3 |
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4.6.6 |
Oh |
U08 |
K13 |
24 |
36 |
14 |
6{4}+8{6} |
8 |
Senpintigita sesedro |
 |
2 3|4 |
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3.8.8 |
Oh |
U09 |
K14 |
24 |
36 |
14 |
8{3}+6{8} |
9 |
Senpintigita dudekedro |
 |
2 5|3 |
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5.6.6 |
Ih |
U25 |
K30 |
60 |
90 |
32 |
12{5}+20{6} |
10 |
Senpintigita dekduedro |
 |
2 3|5 |
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3.10.10 |
Ih |
U26 |
K31 |
60 |
90 |
32 |
20{3}+12{10} |
11 |
Kubokedro |
 |
2|3 4 |
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3.4.3.4 |
Oh |
U07 |
K12 |
12 |
24 |
14 |
8{3}+6{4} |
12 |
Dudek-dekduedro |
 |
2|3 5 |
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3.5.3.5 |
Ih |
U24 |
K29 |
30 |
60 |
32 |
20{3}+12{5} |
13 |
Malgranda rombokub-okedro |
 |
3 4|2 |
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3.4.4.4 |
Oh |
U10 |
K15 |
24 |
48 |
26 |
8{3}+(6+12){4} |
14 |
Malgranda rombo-dudek-dekduedro |
 |
3 5|2 |
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3.4.5.4 |
Ih |
U27 |
K32 |
60 |
120 |
62 |
20{3}+30{4}+12{5} |
15 |
Granda rombokub-okedro
(Rombotranĉita kubokedro)
(Senpintigita kubokedro) |
 |
2 3 4| |
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4.6.8 |
Oh |
U11 |
K16 |
48 |
72 |
26 |
12{4}+8{6}+6{8} |
16 |
Granda rombo-dudek-dekduedro
(Rombotranĉita dudek-dekduedro)
(Senpintigita dudek-dekduedro) |
 |
2 3 5| |
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4.6.10 |
Ih |
U28 |
K33 |
120 |
180 |
62 |
30{4}+20{6}+12{10} |
17 |
Riproĉa malafable kubo |
 |
|2 3 4 |
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3.3.3.3.4 |
O |
U12 |
K17 |
24 |
60 |
38 |
(8+24){3}+6{4} |
18 |
Riproĉa malafable dekduedro |
 |
|2 3 5 |
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3.3.3.3.5 |
I |
U29 |
K34 |
60 |
150 |
92 |
(20+60){3}+12{5} |
[redaktu] Solidoj de Keplero-Poinsot (regulaj stelaj pluredroj) W20, W21, W22, W41
Indekso |
Nomo |
Bildo |
Simbolo de Wythoff |
Vertica figuro
kaj Simbolo de Schläfli |
Geometria simetria grupo |
U# |
K# |
V |
E |
F |
Edroj laŭ speco |
20 |
Malgranda steligita dekduedro |
 |
5|25/2 |
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{5/2,5} |
Ih |
U34 |
K39 |
12 |
30 |
12 |
12{5/2} |
21 |
Granda dekduedro |
 |
5/2|2 5 |
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{5,5/2} |
Ih |
U35 |
K40 |
12 |
30 |
12 |
12{5} |
22 |
Granda steligita dekduedro |
 |
3|25/2 |
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{5/2,3} |
Ih |
U52 |
K57 |
20 |
30 |
12 |
12{5/2} |
41 |
Granda dudekedro
(16-a steligo de dudekedro) |
 |
5/2|2 3 |
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{3,5/2} |
Ih |
U53 |
K58 |
12 |
30 |
20 |
20{3} |
[redaktu] Steligoj W19 ... W66
[redaktu] Steligo de okedro
Indekso |
Nomo |
Geometria simetria grupo |
Bildo |
Facetoj |
2 |
Okedro
(regula) |
Oh |
 |
 |
19 |
Steligita okedro
(Kombinaĵo de du kvaredroj) |
Oh |
 |
 |
[redaktu] Steligoj de dekduedro
Indekso |
Nomo |
Geometria simetria grupo |
Bildo |
Facetoj |
5 |
Dekduedro (regula) |
Ih |
 |
 |
20 |
Malgranda steligita dekduedro (regula)
(Unua steligo de dekduedro) |
Ih |
 |
 |
21 |
Granda dekduedro (regula)
(Dua steligo de dekduedro) |
Ih |
 |
 |
22 |
Granda steligita dekduedro (regula)
(Tria steligo de dekduedro) |
Ih |
 |
 |
[redaktu] Steligoj de dudekedro
Indekso |
Nomo |
Geometria simetria grupo |
Bildo |
Facetoj |
4 |
Dudekedro (regula) |
Ih |
 |
 |
26 |
Unua steligo de dudekedro
(_Triakis_ dudekedro) |
Ih |
 |
 |
23 |
Kombinaĵo de kvin oktedroj
(Unua kombinaĵa steligo de dudekedro) |
Ih |
 |
 |
24 |
Kombinaĵo de kvin kvaredroj
(Dua kombinaĵa steligo de dudekedro) |
I |
 |
 |
25 |
Kombinaĵo de dek kvaredroj
(Tria kombinaĵa steligo de dudekedro) |
Ih |
 |
 |
27 |
Dua steligo de dudekedro |
Ih |
 |
 |
28 |
Tria steligo de dudekedro |
Ih |
 |
 |
29 |
Kvara steligo de dudekedro |
Ih |
 |
 |
30 |
Kvina steligo de dudekedro |
Ih |
 |
 |
31 |
Sesa steligo de dudekedro |
Ih |
 |
 |
32 |
Sepa steligo de dudekedro |
Ih |
 |
 |
33 |
Oka steligo de dudekedro |
Ih |
 |
 |
34 |
Naŭa steligo de dudekedro |
Ih |
 |
 |
35 |
Deka steligo de dudekedro |
I |
 |
 |
36 |
Dek-unua steligo de dudekedro |
I |
 |
 |
37 |
Dek-dua steligo de dudekedro |
Ih |
 |
 |
38 |
Dek-tria steligo de dudekedro |
I |
 |
 |
39 |
Dek-kvara steligo de dudekedro |
I |
 |
 |
40 |
Dek-kvina steligo de dudekedro |
I |
 |
 |
41 |
Granda dudekedro (regula)
(Dek-sesa steligo de dudekedro) |
Ih |
 |
 |
|
42 |
Fina steligo de la dudekedro |
Ih |
 |
 |
[redaktu] Steligoj de kubokedro
Indekso |
Nomo |
Geometria simetria grupo |
Bildo |
Facetoj (okedra (planoj, ebenoj)) |
Facetoj (kubo (planoj, ebenoj)) |
11 |
Kubokedro (regula) |
Oh |
 |
 |
 |
43 |
Kombinaĵo de kubo kaj okedro
(Unua steligo de kubokedro) |
Oh |
 |
 |
 |
44 |
Dua steligo de kubokedro |
Oh |
 |
 |
 |
45 |
Tria steligo de kubokedro |
Oh |
 |
 |
 |
46 |
Kvara steligo de kubokedro |
Oh |
 |
 |
 |
[redaktu] Steligoj de dudek-dekduedro
Indekso |
Nomo |
Geometria simetria grupo |
Bildo |
Facetoj de dudekedraj ebenoj |
Facetoj de dekduedraj ebenoj |
12 |
Dudek-dekduedro
(regula) |
Ih |
 |
 |
 |
47 |
(Unua steligo de dudek-dekduedro)
Kombinaĵo de dekduedro kaj dudekedro |
Ih |
 |
 |
 |
48 |
Dua steligo de dudek-dekduedro |
Ih |
 |
 |
 |
49 |
Tria steligo de dudek-dekduedro |
Ih |
 |
 |
 |
50 |
Kvara steligo de dudek-dekduedro
(Kombinaĵo de malgranda steligita dekduedro
kaj _triakis_ dudekedro) |
Ih |
 |
 |
 |
51 |
Kvina steligo de dudek-dekduedro
(Kombinaĵo de malgranda steligita dekduedro
kaj kvin oktedroj) |
Ih |
 |
 |
 |
52 |
Sesa steligo de dudek-dekduedro |
Ih |
 |
 |
 |
53 |
Sepa steligo de dudek-dekduedro |
Ih |
 |
 |
 |
54 |
Oka steligo de dudek-dekduedro
(Kombinaĵo de kvin kvaredra
kaj granda dekduedro) |
I |
 |
 |
 |
55 |
Naŭa steligo de dudek-dekduedro |
Ih |
 |
 |
 |
56 |
Deka steligo de dudek-dekduedro |
Ih |
 |
 |
 |
57 |
Dek-unua steligo de dudek-dekduedro |
Ih |
 |
 |
 |
58 |
Dek-dua steligo de dudek-dekduedro |
Ih |
 |
 |
 |
59 |
Dek-tria steligo de dudek-dekduedro |
Ih |
 |
 |
 |
60 |
Dek-kvara steligo de dudek-dekduedro |
Ih |
 |
 |
 |
61 |
Kombinaĵo de granda steligita dekduedro kaj granda dudekedro |
Ih |
 |
 |
 |
62 |
Dek-kvina steligo de dudek-dekduedro |
Ih |
 |
 |
 |
63 |
Dek-sesa steligo de dudek-dekduedro |
Ih |
 |
 |
 |
64 |
Dek-sepa steligo de dudek-dekduedro |
Ih |
 |
 |
 |
65 |
Dek-oka steligo de dudek-dekduedro |
Ih |
 |
 |
 |
66 |
Dek-naŭa steligo de dudek-dekduedro |
Ih |
 |
 |
 |
[redaktu] Uniformaj nekonveksaj solidoj W67 ... W119
Indekso |
Nomo |
Bildo |
Simbolo de Wythoff |
Vertica figuro |
Geometria simetria grupo |
U# |
K# |
V |
E |
F |
Edroj laŭ speco |
67 |
Kvar-duon-sesedro |
 |
3/23|2 |

4.3/2.4.3 |
Td |
U04 |
K09 |
6 |
12 |
7 |
4{3}+3{4} |
68 |
Ok-duon-okedro |
 |
3/23|3 |

6.3/2.6.3 |
Oh |
U03 |
K08 |
12 |
24 |
12 |
8{3}+4{6} |
69 |
Malgranda kubokubo-okedro |
 |
3/24|4 |

8.3/2.8.4 |
Oh |
U13 |
K18 |
24 |
48 |
20 |
8{3}+6{4}+6{8} |
70 |
Malgranda du-tritranĉa dudek-dekduedro |
 |
3|5/23 |

(5/2.3)3 |
Ih |
U30 |
K35 |
20 |
60 |
32 |
20{3}+12{5/2} |
71 |
Malgranda dudek-dudek-dekduedro |
 |
5/23|3 |

6.5/2.6.3 |
Ih |
U31 |
K36 |
60 |
120 |
52 |
20{3}+12{5/2}+20{6} |
72 |
Malgranda dekdu-dudek-dekduedro |
 |
3/25|5 |

10.3/2.10.5 |
Ih |
U33 |
K38 |
60 |
120 |
44 |
20{3}+12{5}+12{10} |
73 |
Dekduedro |
 |
2|5/25 |

(5/2.5)2 |
Ih |
U36 |
K41 |
30 |
60 |
24 |
12{5}+12{5/2} |
74 |
Malgranda rombo-dekduedro |
 |
25/25| |

10.4.10/9.4/3 |
Ih |
U39 |
K44 |
60 |
120 |
42 |
30{4}+12{10} |
75 |
Senpintigita granda dekduedro |
 |
25/2|5 |

10.10.5/2 |
Ih |
U37 |
K42 |
60 |
90 |
24 |
12{5/2}+12{10} |
76 |
Rombo-dekdu-dekduedro |
 |
5/25|2 |

4.5/2.4.5 |
Ih |
U38 |
K43 |
60 |
120 |
54 |
30{4}+12{5}+12{5/2} |
77 |
Granda kubokubo-okedro |
 |
3 4|4/3 |

8/3.3.8/3.4 |
Oh |
U14 |
K19 |
24 |
48 |
20 |
8{3}+6{4}+6{8/3} |
78 |
Kubo-duon-okedro |
 |
4/34|3 |

6.4/3.6.4 |
Oh |
U15 |
K20 |
12 |
24 |
10 |
6{4}+4{6} |
79 |
Kubotranĉita kubokedro
(Kubo-oktranĉita kubokedro) |
 |
4/33 4| |

8/3.6.8 |
Oh |
U16 |
K21 |
48 |
72 |
20 |
8{6}+6{8}+6{8/3} |
80 |
Du-tritranĉa dekduedro |
 |
3|5/35 |

(5/3.5)3 |
Ih |
U41 |
K46 |
20 |
60 |
24 |
12{5}+12{5/2} |
81 |
Granda du-tritranĉa dekdu-dudek-dekduedro |
 |
3 5|5/3 |

10/3.3.10/3.5 |
Ih |
U42 |
K47 |
60 |
120 |
44 |
20{3}+12{5}+12{10/3} |
82 |
Malgranda du-tritranĉa dekdu-dudek-dekduedro |
 |
5/33|5 |

10.5/3.10.3 |
Ih |
U43 |
K48 |
60 |
120 |
44 |
20{3}+12{5/2}+12{10} |
83 |
Dudek-dekdu-dekduedro |
 |
5/35|3 |

6.5/3.6.5 |
Ih |
U44 |
K49 |
60 |
120 |
44 |
12{5}+12{5/2}+20{6} |
84 |
Dudektranĉita dekduedro
(Dudek-dekdutranĉita dudek-dekduedro) |
 |
5/33 5| |

10/3.6.10 |
Ih |
U45 |
K50 |
120 |
180 |
44 |
20{6}+12{10}+12{10/3} |
85 |
Uniforma granda rombokub-okedro
(Kvazaŭrombokubo-okedro) |
 |
3/24|2 |

4.3/2.4.4 |
Oh |
U17 |
K22 |
24 |
48 |
26 |
8{3}+(6+12){4} |
86 |
Malgranda rombo-sesedro |
 |
3/22 4| |

4.8.4/3.8 |
Oh |
U18 |
K23 |
24 |
48 |
18 |
12{4}+6{8} |
87 |
Granda du-tritranĉa dudek-dekduedro |
 |
3/2|3 5 |

(5.3.5.3.5.3)/2 |
Ih |
U47 |
K52 |
20 |
60 |
32 |
20{3}+12{5} |
88 |
Granda dudek-dudek-dekduedro |
 |
3/25|3 |

6.3/2.6.5 |
Ih |
U48 |
K53 |
60 |
120 |
52 |
20{3}+12{5}+20{6} |
89 |
Malgranda dudek-duon-dekduedro |
 |
3/23|5 |

10.3/2.10.3 |
Ih |
U49 |
K54 |
30 |
60 |
26 |
20{3}+6{10} |
90 |
Malgranda dekdu-dudekedro |
 |
3/23 5| |

10.6.10/9.6/5 |
Ih |
U50 |
K55 |
60 |
120 |
32 |
20{6}+12{10} |
91 |
Malgranda dekdu-duon-dekduedro |
 |
5/45|5 |

10.5/4.10.5 |
Ih |
U51 |
K56 |
30 |
60 |
18 |
12{5}+6{10} |
92 |
Steligita senpintigita sesedro
(Kvazaŭtranĉita sesedro) |
 |
2 3|4/3 |

8/3.8/3.3 |
Oh |
U19 |
K24 |
24 |
36 |
14 |
8{3}+6{8/3} |
93 |
Granda senpintigita kubokedro
(Kvazaŭtranĉita kubokedro) |
 |
4/32 3| |

8/3.4.6 |
Oh |
U20 |
K25 |
48 |
72 |
26 |
12{4}+8{6}+6{8/3} |
94 |
Granda dudek-dekduedro |
 |
2|5/23 |

(5/2.3)2 |
Ih |
U54 |
K59 |
30 |
60 |
32 |
20{3}+12{5/2} |
95 |
Senpintigita granda dudekedro |
 |
25/2|3 |

6.6.5/2 |
Ih |
U55 |
K60 |
60 |
90 |
32 |
12{5/2}+20{6} |
96 |
Rombo-dudekedro |
 |
25/23| |

6.4.6/5.4/3 |
Ih |
U56 |
K61 |
60 |
120 |
50 |
30{4}+20{6} |
97 |
Malgranda steligita senpintigita dekduedro
(Kvazaŭtranĉita malgranda steligita dekduedro) |
 |
2 5|5/3 |

10/3.10/3.5 |
Ih |
U58 |
K63 |
60 |
90 |
24 |
12{5}+12{10/3} |
98 |
Senpintigita dekduedro
(Kvazaŭtranĉita dekduedro) |
 |
5/32 5| |

10/3.4.10 |
Ih |
U59 |
K64 |
120 |
180 |
54 |
30{4}+12{10}+12{10/3} |
99 |
Granda dekdu-dudek-dekduedro |
 |
5/23|5/3 |

10/3.5/2.10/3.3 |
Ih |
U61 |
K66 |
60 |
120 |
44 |
20{3}+12{5/2}+12{10/3 } |
100 |
Malgranda dekdu-duon-dudekedro |
 |
5/35/2|3 |

6.5/3.6.5/2 |
Ih |
U62 |
K67 |
30 |
60 |
22 |
12{5/2}+10{6} |
101 |
Granda dekdu-dudekedro |
 |
5/35/23| |

6.10/3.6/5.10/7 |
Ih |
U63 |
K68 |
60 |
120 |
32 |
20{6}+12{10/3} |
102 |
Granda dekdu-duon-dudekedro |
 |
5/45|3 |

6.5/4.6.5 |
Ih |
U65 |
K70 |
30 |
60 |
22 |
12{5}+10{6} |
103 |
Granda rombo-sesedro |
 |
4/33/22| |

4.8/3.4/3.8/5 |
Oh |
U21 |
K26 |
24 |
48 |
18 |
12{4}+6{8/3} |
104 |
Granda steligita senpintigita dekduedro
(Kvazaŭtranĉita granda steligita dekduedro) |
 |
2 3|5/3 |

10/3.10/3.3 |
Ih |
U66 |
K71 |
60 |
90 |
32 |
20{3}+12{10/3} |
105 |
Uniforma granda rombo-dudek-dekduedro
(Kvazaŭrombo-dudek-dekduedro) |
 |
5/33|2 |

4.5/3.4.3 |
Ih |
U67 |
K72 |
60 |
120 |
62 |
20{3}+30{4}+12{5/2} |
106 |
Granda dudek-duon-dekduedro |
 |
3 3|5/3 |

10/3.3/2.10/3.3 |
Ih |
U71 |
K76 |
30 |
60 |
26 |
20{3}+6{10/3} |
107 |
Granda dekdu-duon-dekduedro |
 |
5/35/2|5/3 |

10/3.5/3.10/3.5/2 |
Ih |
U70 |
K75 |
30 |
60 |
18 |
12{5/2}+6{10/3} |
108 |
Granda senpintigita dudek-dekduedro
(Granda kvazaŭtranĉita dudek-dekduedro) |
 |
5/32 3| |

10/3.4.6 |
Ih |
U68 |
K73 |
120 |
180 |
62 |
30{4}+20{6}+12{10/3} |
109 |
Granda rombo-dekduedro |
 |
3/25/32| |

4.10/3.4/3.10/7 |
Ih |
U73 |
K78 |
60 |
120 |
42 |
30{4}+12{10/3} |
110 |
Malgranda riproĉa malafable dudek-dudek-dekduedro |
 |
|5/23 3 |
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3.3.3.3.3.5/2 |
Ih |
U32 |
K37 |
60 |
180 |
112 |
(40+60){3}+12{5/2} |
111 |
Riproĉa malafable dekduedro |
 |
|25/25 |
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3.3.5/2.3.5 |
I |
U40 |
K45 |
60 |
150 |
84 |
60{3}+12{5}+12{5/2} |
112 |
Riproĉa malafable dudek-dekdu-dekduedro |
 |
|5/33 5 |
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3.3.3.3.5.5/3 |
I |
U46 |
K51 |
60 |
180 |
104 |
(20+6){3}+12{5}+12{5/2} |
113 |
Granda inversigita riproĉa malafable dudek-dekduedro |
 |
|5/32 3 |
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3.3.3.3.5/3 |
I |
U69 |
K74 |
60 |
150 |
92 |
(20+60){3}+12{5/2} |
114 |
Inversigita riproĉa malafable dekduedro |
 |
|5/32 5 |
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3.5/3.3.3.5 |
I |
U60 |
K65 |
60 |
150 |
84 |
60{3}+12{5}+12{5/2} |
115 |
Granda riproĉa malafable dekdu-dudek-dekduedro |
 |
|5/35/23 |
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3.5/3.3.5/2.3.3 |
I |
U64 |
K69 |
60 |
180 |
104 |
(20+60){3}+(12+12){5/2} |
116 |
Granda riproĉa malafable dudek-dekduedro |
 |
|25/25/2 |
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3.3.3.3.5/2 |
I |
U57 |
K62 |
60 |
150 |
92 |
(20+60){3}+12{5/2} |
117 |
Granda malantaŭe riproĉa malafable dudek-dekduedro |
 |
|3/25/32 |
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(3.3.3.3.5/3)/2 |
I |
U74 |
K79 |
60 |
150 |
92 |
(20+60){3}+12{5/2} |
118 |
Malgranda malantaŭe riproĉa malafable dudek-dudek-dekduedro |
 |
|3/23/25/2 |
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(3.3.3.3.3.5/2)/2 |
Ih |
U72 |
K77 |
180 |
60 |
112 |
(40+60){3}+12{5/2} |
119 |
Granda durombo-dudek-dekduedro |
 |
|3/25/335/2 |
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(4.5/3.4.3.4.5/2.4.3/2)/2 |
Ih |
U75 |
K80 |
60 |
240 |
124 |
40{3}+60{4}+24{5/2} |
[redaktu] Eksteraj ligiloj