Polytope of Type {12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12}*24
Also Known As : dodecagon, {12}. if this polytope has another name.
Group : SmallGroup(24,6)
Rank : 2
Schlafli Type : {12}
Number of vertices, edges, etc : 12, 12
Order of s0s1 : 12
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,2} of size 48
{12,4} of size 96
{12,4} of size 96
{12,4} of size 96
{12,3} of size 96
{12,6} of size 144
{12,6} of size 144
{12,6} of size 144
{12,3} of size 144
{12,6} of size 144
{12,4} of size 192
{12,8} of size 192
{12,8} of size 192
{12,4} of size 192
{12,4} of size 192
{12,6} of size 192
{12,6} of size 192
{12,4} of size 216
{12,6} of size 216
{12,6} of size 216
{12,6} of size 216
{12,10} of size 240
{12,12} of size 288
{12,12} of size 288
{12,12} of size 288
{12,3} of size 288
{12,4} of size 288
{12,6} of size 288
{12,6} of size 288
{12,14} of size 336
{12,8} of size 384
{12,4} of size 384
{12,8} of size 384
{12,16} of size 384
{12,16} of size 384
{12,4} of size 384
{12,4} of size 384
{12,3} of size 384
{12,8} of size 384
{12,8} of size 384
{12,4} of size 384
{12,12} of size 384
{12,8} of size 384
{12,12} of size 384
{12,8} of size 384
{12,6} of size 384
{12,8} of size 384
{12,8} of size 384
{12,12} of size 384
{12,12} of size 384
{12,4} of size 384
{12,18} of size 432
{12,6} of size 432
{12,6} of size 432
{12,18} of size 432
{12,6} of size 432
{12,9} of size 432
{12,18} of size 432
{12,3} of size 432
{12,6} of size 432
{12,4} of size 432
{12,6} of size 432
{12,6} of size 432
{12,6} of size 432
{12,4} of size 432
{12,6} of size 432
{12,6} of size 432
{12,20} of size 480
{12,4} of size 480
{12,4} of size 480
{12,6} of size 480
{12,6} of size 480
{12,10} of size 480
{12,10} of size 480
{12,10} of size 480
{12,10} of size 480
{12,5} of size 480
{12,15} of size 480
{12,22} of size 528
{12,24} of size 576
{12,12} of size 576
{12,12} of size 576
{12,12} of size 576
{12,24} of size 576
{12,24} of size 576
{12,24} of size 576
{12,24} of size 576
{12,24} of size 576
{12,4} of size 576
{12,8} of size 576
{12,8} of size 576
{12,12} of size 576
{12,12} of size 576
{12,12} of size 576
{12,12} of size 576
{12,6} of size 576
{12,6} of size 576
{12,12} of size 576
{12,12} of size 576
{12,6} of size 576
{12,6} of size 576
{12,6} of size 576
{12,6} of size 576
{12,12} of size 576
{12,12} of size 576
{12,3} of size 576
{12,12} of size 576
{12,10} of size 600
{12,26} of size 624
{12,6} of size 648
{12,12} of size 648
{12,3} of size 648
{12,9} of size 648
{12,9} of size 648
{12,28} of size 672
{12,21} of size 672
{12,30} of size 720
{12,30} of size 720
{12,30} of size 720
{12,6} of size 720
{12,6} of size 720
{12,10} of size 720
{12,15} of size 720
{12,30} of size 720
{12,8} of size 768
{12,16} of size 768
{12,16} of size 768
{12,32} of size 768
{12,32} of size 768
{12,4} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,6} of size 768
{12,6} of size 768
{12,8} of size 768
{12,8} of size 768
{12,6} of size 768
{12,8} of size 768
{12,6} of size 768
{12,6} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,24} of size 768
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{12,4} of size 768
{12,4} of size 768
{12,6} of size 768
{12,8} of size 768
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{12,8} of size 768
{12,12} of size 768
{12,4} of size 768
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{12,8} of size 768
{12,12} of size 768
{12,8} of size 768
{12,24} of size 768
{12,4} of size 768
{12,24} of size 768
{12,6} of size 768
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{12,8} of size 768
{12,24} of size 768
{12,4} of size 768
{12,24} of size 768
{12,6} of size 768
{12,8} of size 768
{12,6} of size 768
{12,4} of size 768
{12,6} of size 768
{12,4} of size 768
{12,34} of size 816
{12,36} of size 864
{12,36} of size 864
{12,12} of size 864
{12,12} of size 864
{12,12} of size 864
{12,9} of size 864
{12,3} of size 864
{12,4} of size 864
{12,4} of size 864
{12,12} of size 864
{12,12} of size 864
{12,12} of size 864
{12,12} of size 864
{12,12} of size 864
{12,18} of size 864
{12,18} of size 864
{12,6} of size 864
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{12,4} of size 864
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{12,12} of size 864
{12,12} of size 864
{12,12} of size 864
{12,6} of size 864
{12,38} of size 912
{12,20} of size 960
{12,40} of size 960
{12,40} of size 960
{12,10} of size 960
{12,4} of size 960
{12,6} of size 960
{12,4} of size 960
{12,6} of size 960
{12,10} of size 960
{12,10} of size 960
{12,10} of size 960
{12,20} of size 960
{12,30} of size 960
{12,20} of size 960
{12,30} of size 960
{12,10} of size 960
{12,42} of size 1008
{12,42} of size 1008
{12,42} of size 1008
{12,8} of size 1008
{12,21} of size 1008
{12,42} of size 1008
{12,44} of size 1056
{12,33} of size 1056
{12,46} of size 1104
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,8} of size 1152
{12,48} of size 1152
{12,48} of size 1152
{12,48} of size 1152
{12,16} of size 1152
{12,48} of size 1152
{12,48} of size 1152
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{12,16} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,12} of size 1152
{12,24} of size 1152
{12,4} of size 1152
{12,8} of size 1152
{12,3} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,24} of size 1152
{12,6} of size 1152
{12,24} of size 1152
{12,6} of size 1152
{12,6} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,6} of size 1152
{12,24} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,24} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,6} of size 1152
{12,24} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,24} of size 1152
{12,12} of size 1152
{12,12} of size 1152
{12,24} of size 1152
{12,6} of size 1152
{12,24} of size 1152
{12,3} of size 1152
{12,6} of size 1152
{12,24} of size 1152
{12,24} of size 1152
{12,6} of size 1152
{12,6} of size 1152
{12,4} of size 1152
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{12,6} of size 1152
{12,12} of size 1152
{12,14} of size 1176
{12,50} of size 1200
{12,6} of size 1200
{12,10} of size 1200
{12,10} of size 1200
{12,6} of size 1200
{12,4} of size 1200
{12,10} of size 1200
{12,52} of size 1248
{12,39} of size 1248
{12,18} of size 1296
{12,54} of size 1296
{12,6} of size 1296
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{12,18} of size 1296
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{12,6} of size 1296
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{12,18} of size 1296
{12,18} of size 1296
{12,6} of size 1296
{12,27} of size 1296
{12,54} of size 1296
{12,3} of size 1296
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{12,9} of size 1296
{12,18} of size 1296
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{12,9} of size 1296
{12,18} of size 1296
{12,6} of size 1296
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{12,6} of size 1296
{12,6} of size 1296
{12,6} of size 1296
{12,4} of size 1296
{12,6} of size 1296
{12,6} of size 1296
{12,6} of size 1296
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{12,12} of size 1296
{12,12} of size 1296
{12,12} of size 1296
{12,12} of size 1296
{12,6} of size 1296
{12,12} of size 1296
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{12,3} of size 1296
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{12,6} of size 1296
{12,9} of size 1296
{12,9} of size 1296
{12,18} of size 1296
{12,18} of size 1296
{12,18} of size 1296
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{12,6} of size 1296
{12,12} of size 1296
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{12,12} of size 1296
{12,3} of size 1320
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{12,4} of size 1320
{12,4} of size 1320
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{12,5} of size 1320
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{12,10} of size 1320
{12,10} of size 1320
{12,10} of size 1320
{12,11} of size 1320
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{12,12} of size 1320
{12,12} of size 1320
{12,28} of size 1344
{12,56} of size 1344
{12,56} of size 1344
{12,8} of size 1344
{12,8} of size 1344
{12,7} of size 1344
{12,4} of size 1344
{12,4} of size 1344
{12,6} of size 1344
{12,6} of size 1344
{12,8} of size 1344
{12,8} of size 1344
{12,8} of size 1344
{12,8} of size 1344
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{12,8} of size 1344
{12,28} of size 1344
{12,42} of size 1344
{12,28} of size 1344
{12,42} of size 1344
{12,58} of size 1392
{12,60} of size 1440
{12,60} of size 1440
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{12,6} of size 1440
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{12,10} of size 1440
{12,10} of size 1440
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{12,10} of size 1440
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{12,15} of size 1440
{12,15} of size 1440
{12,15} of size 1440
{12,20} of size 1440
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{12,6} of size 1440
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{12,10} of size 1440
{12,30} of size 1440
{12,30} of size 1440
{12,62} of size 1488
{12,66} of size 1584
{12,66} of size 1584
{12,66} of size 1584
{12,33} of size 1584
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{12,68} of size 1632
{12,51} of size 1632
{12,70} of size 1680
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{12,12} of size 1728
{12,12} of size 1728
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{12,6} of size 1728
{12,12} of size 1728
{12,12} of size 1728
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{12,6} of size 1728
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{12,6} of size 1728
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{12,12} of size 1920
{12,20} of size 1920
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{12,9} of size 1944
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{12,82} of size 1968
Vertex Figure Of :
{2,12} of size 48
{4,12} of size 96
{4,12} of size 96
{4,12} of size 96
{3,12} of size 96
{6,12} of size 144
{6,12} of size 144
{6,12} of size 144
{3,12} of size 144
{6,12} of size 144
{4,12} of size 192
{8,12} of size 192
{8,12} of size 192
{4,12} of size 192
{4,12} of size 192
{6,12} of size 192
{6,12} of size 192
{4,12} of size 216
{6,12} of size 216
{6,12} of size 216
{6,12} of size 216
{10,12} of size 240
{12,12} of size 288
{12,12} of size 288
{12,12} of size 288
{3,12} of size 288
{4,12} of size 288
{6,12} of size 288
{6,12} of size 288
{14,12} of size 336
{8,12} of size 384
{4,12} of size 384
{8,12} of size 384
{16,12} of size 384
{16,12} of size 384
{4,12} of size 384
{4,12} of size 384
{3,12} of size 384
{8,12} of size 384
{8,12} of size 384
{4,12} of size 384
{12,12} of size 384
{8,12} of size 384
{12,12} of size 384
{8,12} of size 384
{6,12} of size 384
{8,12} of size 384
{8,12} of size 384
{12,12} of size 384
{12,12} of size 384
{4,12} of size 384
{18,12} of size 432
{6,12} of size 432
{6,12} of size 432
{18,12} of size 432
{6,12} of size 432
{9,12} of size 432
{18,12} of size 432
{3,12} of size 432
{6,12} of size 432
{4,12} of size 432
{6,12} of size 432
{6,12} of size 432
{6,12} of size 432
{4,12} of size 432
{6,12} of size 432
{6,12} of size 432
{20,12} of size 480
{4,12} of size 480
{4,12} of size 480
{6,12} of size 480
{6,12} of size 480
{10,12} of size 480
{10,12} of size 480
{10,12} of size 480
{10,12} of size 480
{5,12} of size 480
{15,12} of size 480
{22,12} of size 528
{24,12} of size 576
{12,12} of size 576
{12,12} of size 576
{12,12} of size 576
{24,12} of size 576
{24,12} of size 576
{24,12} of size 576
{24,12} of size 576
{24,12} of size 576
{4,12} of size 576
{8,12} of size 576
{8,12} of size 576
{12,12} of size 576
{12,12} of size 576
{12,12} of size 576
{12,12} of size 576
{6,12} of size 576
{6,12} of size 576
{12,12} of size 576
{12,12} of size 576
{6,12} of size 576
{6,12} of size 576
{6,12} of size 576
{6,12} of size 576
{12,12} of size 576
{12,12} of size 576
{3,12} of size 576
{12,12} of size 576
{10,12} of size 600
{26,12} of size 624
{6,12} of size 648
{12,12} of size 648
{3,12} of size 648
{9,12} of size 648
{9,12} of size 648
{28,12} of size 672
{21,12} of size 672
{30,12} of size 720
{30,12} of size 720
{30,12} of size 720
{6,12} of size 720
{6,12} of size 720
{10,12} of size 720
{15,12} of size 720
{30,12} of size 720
{8,12} of size 768
{16,12} of size 768
{16,12} of size 768
{32,12} of size 768
{32,12} of size 768
{4,12} of size 768
{8,12} of size 768
{8,12} of size 768
{8,12} of size 768
{8,12} of size 768
{8,12} of size 768
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{8,12} of size 768
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Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6}*12
3-fold quotients : {4}*8
4-fold quotients : {3}*6
6-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {24}*48
3-fold covers : {36}*72
4-fold covers : {48}*96
5-fold covers : {60}*120
6-fold covers : {72}*144
7-fold covers : {84}*168
8-fold covers : {96}*192
9-fold covers : {108}*216
10-fold covers : {120}*240
11-fold covers : {132}*264
12-fold covers : {144}*288
13-fold covers : {156}*312
14-fold covers : {168}*336
15-fold covers : {180}*360
16-fold covers : {192}*384
17-fold covers : {204}*408
18-fold covers : {216}*432
19-fold covers : {228}*456
20-fold covers : {240}*480
21-fold covers : {252}*504
22-fold covers : {264}*528
23-fold covers : {276}*552
24-fold covers : {288}*576
25-fold covers : {300}*600
26-fold covers : {312}*624
27-fold covers : {324}*648
28-fold covers : {336}*672
29-fold covers : {348}*696
30-fold covers : {360}*720
31-fold covers : {372}*744
32-fold covers : {384}*768
33-fold covers : {396}*792
34-fold covers : {408}*816
35-fold covers : {420}*840
36-fold covers : {432}*864
37-fold covers : {444}*888
38-fold covers : {456}*912
39-fold covers : {468}*936
40-fold covers : {480}*960
41-fold covers : {492}*984
42-fold covers : {504}*1008
43-fold covers : {516}*1032
44-fold covers : {528}*1056
45-fold covers : {540}*1080
46-fold covers : {552}*1104
47-fold covers : {564}*1128
48-fold covers : {576}*1152
49-fold covers : {588}*1176
50-fold covers : {600}*1200
51-fold covers : {612}*1224
52-fold covers : {624}*1248
53-fold covers : {636}*1272
54-fold covers : {648}*1296
55-fold covers : {660}*1320
56-fold covers : {672}*1344
57-fold covers : {684}*1368
58-fold covers : {696}*1392
59-fold covers : {708}*1416
60-fold covers : {720}*1440
61-fold covers : {732}*1464
62-fold covers : {744}*1488
63-fold covers : {756}*1512
65-fold covers : {780}*1560
66-fold covers : {792}*1584
67-fold covers : {804}*1608
68-fold covers : {816}*1632
69-fold covers : {828}*1656
70-fold covers : {840}*1680
71-fold covers : {852}*1704
72-fold covers : {864}*1728
73-fold covers : {876}*1752
74-fold covers : {888}*1776
75-fold covers : {900}*1800
76-fold covers : {912}*1824
77-fold covers : {924}*1848
78-fold covers : {936}*1872
79-fold covers : {948}*1896
80-fold covers : {960}*1920
81-fold covers : {972}*1944
82-fold covers : {984}*1968
83-fold covers : {996}*1992
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(12)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(12)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
poly := sub<Sym(12)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope