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# Polytope of Type {5,2}

Atlas Canonical Name : {5,2}*20
if this polytope has a name.
Group : SmallGroup(20,4)
Rank : 3
Schlafli Type : {5,2}
Number of vertices, edges, etc : 5, 5, 2
Order of s0s1s2 : 10
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,2,2} of size 40
{5,2,3} of size 60
{5,2,4} of size 80
{5,2,5} of size 100
{5,2,6} of size 120
{5,2,7} of size 140
{5,2,8} of size 160
{5,2,9} of size 180
{5,2,10} of size 200
{5,2,11} of size 220
{5,2,12} of size 240
{5,2,13} of size 260
{5,2,14} of size 280
{5,2,15} of size 300
{5,2,16} of size 320
{5,2,17} of size 340
{5,2,18} of size 360
{5,2,19} of size 380
{5,2,20} of size 400
{5,2,21} of size 420
{5,2,22} of size 440
{5,2,23} of size 460
{5,2,24} of size 480
{5,2,25} of size 500
{5,2,26} of size 520
{5,2,27} of size 540
{5,2,28} of size 560
{5,2,29} of size 580
{5,2,30} of size 600
{5,2,31} of size 620
{5,2,32} of size 640
{5,2,33} of size 660
{5,2,34} of size 680
{5,2,35} of size 700
{5,2,36} of size 720
{5,2,37} of size 740
{5,2,38} of size 760
{5,2,39} of size 780
{5,2,40} of size 800
{5,2,41} of size 820
{5,2,42} of size 840
{5,2,43} of size 860
{5,2,44} of size 880
{5,2,45} of size 900
{5,2,46} of size 920
{5,2,47} of size 940
{5,2,48} of size 960
{5,2,49} of size 980
{5,2,50} of size 1000
{5,2,51} of size 1020
{5,2,52} of size 1040
{5,2,53} of size 1060
{5,2,54} of size 1080
{5,2,55} of size 1100
{5,2,56} of size 1120
{5,2,57} of size 1140
{5,2,58} of size 1160
{5,2,59} of size 1180
{5,2,60} of size 1200
{5,2,61} of size 1220
{5,2,62} of size 1240
{5,2,63} of size 1260
{5,2,64} of size 1280
{5,2,65} of size 1300
{5,2,66} of size 1320
{5,2,67} of size 1340
{5,2,68} of size 1360
{5,2,69} of size 1380
{5,2,70} of size 1400
{5,2,71} of size 1420
{5,2,72} of size 1440
{5,2,73} of size 1460
{5,2,74} of size 1480
{5,2,75} of size 1500
{5,2,76} of size 1520
{5,2,77} of size 1540
{5,2,78} of size 1560
{5,2,79} of size 1580
{5,2,80} of size 1600
{5,2,81} of size 1620
{5,2,82} of size 1640
{5,2,83} of size 1660
{5,2,84} of size 1680
{5,2,85} of size 1700
{5,2,86} of size 1720
{5,2,87} of size 1740
{5,2,88} of size 1760
{5,2,89} of size 1780
{5,2,90} of size 1800
{5,2,91} of size 1820
{5,2,92} of size 1840
{5,2,93} of size 1860
{5,2,94} of size 1880
{5,2,95} of size 1900
{5,2,96} of size 1920
{5,2,97} of size 1940
{5,2,98} of size 1960
{5,2,99} of size 1980
{5,2,100} of size 2000
Vertex Figure Of :
{2,5,2} of size 40
{3,5,2} of size 120
{5,5,2} of size 120
{10,5,2} of size 200
{4,5,2} of size 240
{6,5,2} of size 240
{3,5,2} of size 240
{5,5,2} of size 240
{6,5,2} of size 240
{6,5,2} of size 240
{10,5,2} of size 240
{10,5,2} of size 240
{4,5,2} of size 320
{5,5,2} of size 320
{4,5,2} of size 480
{6,5,2} of size 480
{6,5,2} of size 480
{10,5,2} of size 480
{5,5,2} of size 640
{8,5,2} of size 640
{8,5,2} of size 640
{10,5,2} of size 640
{4,5,2} of size 640
{10,5,2} of size 640
{6,5,2} of size 960
{8,5,2} of size 960
{12,5,2} of size 960
{20,5,2} of size 960
{10,5,2} of size 1000
{5,5,2} of size 1200
{6,5,2} of size 1200
{10,5,2} of size 1200
{15,5,2} of size 1200
{8,5,2} of size 1280
{10,5,2} of size 1280
{4,5,2} of size 1280
{8,5,2} of size 1280
{20,5,2} of size 1280
{20,5,2} of size 1280
{5,5,2} of size 1320
{6,5,2} of size 1320
{6,5,2} of size 1440
{4,5,2} of size 1440
{5,5,2} of size 1440
{8,5,2} of size 1440
{8,5,2} of size 1440
{10,5,2} of size 1440
{5,5,2} of size 1920
{6,5,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,2}*40
3-fold covers : {15,2}*60
4-fold covers : {20,2}*80, {10,4}*80
5-fold covers : {25,2}*100, {5,10}*100
6-fold covers : {10,6}*120, {30,2}*120
7-fold covers : {35,2}*140
8-fold covers : {20,4}*160, {40,2}*160, {10,8}*160
9-fold covers : {45,2}*180, {15,6}*180
10-fold covers : {50,2}*200, {10,10}*200a, {10,10}*200c
11-fold covers : {55,2}*220
12-fold covers : {10,12}*240, {20,6}*240a, {60,2}*240, {30,4}*240a, {15,6}*240, {15,4}*240
13-fold covers : {65,2}*260
14-fold covers : {10,14}*280, {70,2}*280
15-fold covers : {75,2}*300, {15,10}*300
16-fold covers : {40,4}*320a, {20,4}*320, {40,4}*320b, {20,8}*320a, {20,8}*320b, {80,2}*320, {10,16}*320, {5,4}*320
17-fold covers : {85,2}*340
18-fold covers : {10,18}*360, {90,2}*360, {30,6}*360a, {30,6}*360b, {30,6}*360c
19-fold covers : {95,2}*380
20-fold covers : {100,2}*400, {50,4}*400, {10,20}*400a, {20,10}*400a, {20,10}*400b, {10,20}*400c
21-fold covers : {105,2}*420
22-fold covers : {10,22}*440, {110,2}*440
23-fold covers : {115,2}*460
24-fold covers : {10,24}*480, {40,6}*480, {20,12}*480, {60,4}*480a, {120,2}*480, {30,8}*480, {15,12}*480, {15,8}*480, {20,6}*480c, {30,6}*480, {30,4}*480
25-fold covers : {125,2}*500, {25,10}*500, {5,10}*500
26-fold covers : {10,26}*520, {130,2}*520
27-fold covers : {135,2}*540, {45,6}*540, {15,6}*540
28-fold covers : {20,14}*560, {10,28}*560, {140,2}*560, {70,4}*560
29-fold covers : {145,2}*580
30-fold covers : {50,6}*600, {150,2}*600, {10,30}*600a, {10,30}*600b, {30,10}*600b, {30,10}*600c
31-fold covers : {155,2}*620
32-fold covers : {40,4}*640a, {40,8}*640a, {40,8}*640b, {20,8}*640a, {40,8}*640c, {40,8}*640d, {80,4}*640a, {80,4}*640b, {20,4}*640a, {40,4}*640b, {20,8}*640b, {20,16}*640a, {20,16}*640b, {160,2}*640, {10,32}*640, {5,8}*640a, {5,4}*640, {5,8}*640b, {10,4}*640a, {10,4}*640b
33-fold covers : {165,2}*660
34-fold covers : {10,34}*680, {170,2}*680
35-fold covers : {175,2}*700, {35,10}*700
36-fold covers : {10,36}*720, {20,18}*720a, {180,2}*720, {90,4}*720a, {45,4}*720, {60,6}*720a, {30,12}*720a, {30,12}*720b, {60,6}*720b, {60,6}*720c, {30,12}*720c, {20,4}*720, {30,4}*720, {15,12}*720, {15,6}*720e, {20,6}*720
37-fold covers : {185,2}*740
38-fold covers : {10,38}*760, {190,2}*760
39-fold covers : {195,2}*780
40-fold covers : {100,4}*800, {200,2}*800, {50,8}*800, {10,40}*800a, {40,10}*800a, {40,10}*800b, {20,20}*800a, {20,20}*800c, {10,40}*800c
41-fold covers : {205,2}*820
42-fold covers : {30,14}*840, {10,42}*840, {70,6}*840, {210,2}*840
43-fold covers : {215,2}*860
44-fold covers : {20,22}*880, {10,44}*880, {220,2}*880, {110,4}*880
45-fold covers : {225,2}*900, {75,6}*900, {45,10}*900, {15,30}*900
46-fold covers : {10,46}*920, {230,2}*920
47-fold covers : {235,2}*940
48-fold covers : {10,48}*960, {80,6}*960, {20,12}*960a, {20,24}*960a, {40,12}*960a, {20,24}*960b, {40,12}*960b, {120,4}*960a, {60,4}*960a, {120,4}*960b, {60,8}*960a, {60,8}*960b, {240,2}*960, {30,16}*960, {15,6}*960, {15,8}*960a, {20,12}*960b, {20,6}*960e, {60,6}*960a, {30,12}*960a, {30,6}*960, {40,6}*960d, {40,6}*960e, {60,6}*960b, {20,12}*960c, {30,12}*960b, {60,4}*960b, {30,4}*960b, {60,4}*960c, {30,8}*960b, {30,8}*960c, {15,4}*960
49-fold covers : {245,2}*980, {35,14}*980
50-fold covers : {250,2}*1000, {10,50}*1000a, {50,10}*1000a, {50,10}*1000b, {10,10}*1000a, {10,10}*1000c, {10,10}*1000d
51-fold covers : {255,2}*1020
52-fold covers : {20,26}*1040, {10,52}*1040, {260,2}*1040, {130,4}*1040
53-fold covers : {265,2}*1060
54-fold covers : {10,54}*1080, {270,2}*1080, {30,18}*1080a, {30,6}*1080a, {90,6}*1080a, {90,6}*1080b, {30,18}*1080b, {30,6}*1080b, {30,6}*1080c, {30,6}*1080d
55-fold covers : {275,2}*1100, {55,10}*1100
56-fold covers : {40,14}*1120, {10,56}*1120, {20,28}*1120, {140,4}*1120, {280,2}*1120, {70,8}*1120
57-fold covers : {285,2}*1140
58-fold covers : {10,58}*1160, {290,2}*1160
59-fold covers : {295,2}*1180
60-fold covers : {50,12}*1200, {100,6}*1200a, {300,2}*1200, {150,4}*1200a, {75,6}*1200, {75,4}*1200, {20,30}*1200a, {10,60}*1200a, {20,30}*1200b, {30,20}*1200b, {10,60}*1200b, {60,10}*1200b, {60,10}*1200c, {30,20}*1200c, {5,4}*1200, {5,6}*1200a, {5,6}*1200b, {5,10}*1200a, {15,10}*1200a, {15,20}*1200, {15,30}*1200
61-fold covers : {305,2}*1220
62-fold covers : {10,62}*1240, {310,2}*1240
63-fold covers : {315,2}*1260, {105,6}*1260
64-fold covers : {40,8}*1280a, {20,8}*1280a, {40,8}*1280b, {40,4}*1280a, {40,8}*1280c, {40,8}*1280d, {20,16}*1280a, {80,4}*1280a, {20,16}*1280b, {80,4}*1280b, {80,8}*1280a, {40,16}*1280a, {80,8}*1280b, {40,16}*1280b, {40,16}*1280c, {80,8}*1280c, {80,8}*1280d, {40,16}*1280d, {40,16}*1280e, {80,8}*1280e, {80,8}*1280f, {40,16}*1280f, {20,32}*1280a, {160,4}*1280a, {20,32}*1280b, {160,4}*1280b, {20,4}*1280a, {40,4}*1280b, {20,8}*1280b, {20,8}*1280c, {40,8}*1280e, {40,4}*1280c, {40,4}*1280d, {20,8}*1280d, {40,8}*1280f, {40,8}*1280g, {40,8}*1280h, {10,64}*1280, {320,2}*1280, {5,8}*1280, {10,8}*1280a, {10,8}*1280b, {10,4}*1280a, {20,4}*1280b, {20,4}*1280c, {10,8}*1280c, {10,4}*1280b, {10,8}*1280d, {20,4}*1280d, {20,4}*1280e, {10,4}*1280c, {10,8}*1280e, {10,8}*1280f
65-fold covers : {325,2}*1300, {65,10}*1300
66-fold covers : {30,22}*1320, {10,66}*1320, {110,6}*1320, {330,2}*1320
67-fold covers : {335,2}*1340
68-fold covers : {20,34}*1360, {10,68}*1360, {340,2}*1360, {170,4}*1360
69-fold covers : {345,2}*1380
70-fold covers : {50,14}*1400, {350,2}*1400, {10,70}*1400a, {10,70}*1400b, {70,10}*1400b, {70,10}*1400c
71-fold covers : {355,2}*1420
72-fold covers : {10,72}*1440, {40,18}*1440, {20,36}*1440, {180,4}*1440a, {360,2}*1440, {90,8}*1440, {45,8}*1440, {120,6}*1440a, {30,24}*1440a, {60,12}*1440a, {30,24}*1440b, {120,6}*1440b, {120,6}*1440c, {60,12}*1440b, {60,12}*1440c, {30,24}*1440c, {20,18}*1440, {90,4}*1440, {20,4}*1440, {60,4}*1440, {30,8}*1440, {15,24}*1440, {15,12}*1440c, {40,6}*1440, {20,12}*1440, {30,6}*1440g, {60,6}*1440c, {30,12}*1440a, {30,12}*1440b, {30,6}*1440h, {60,6}*1440d
73-fold covers : {365,2}*1460
74-fold covers : {10,74}*1480, {370,2}*1480
75-fold covers : {375,2}*1500, {75,10}*1500, {15,10}*1500e, {15,6}*1500b, {15,10}*1500g
76-fold covers : {20,38}*1520, {10,76}*1520, {380,2}*1520, {190,4}*1520
77-fold covers : {385,2}*1540
78-fold covers : {30,26}*1560, {10,78}*1560, {130,6}*1560, {390,2}*1560
79-fold covers : {395,2}*1580
80-fold covers : {200,4}*1600a, {100,4}*1600, {200,4}*1600b, {100,8}*1600a, {100,8}*1600b, {400,2}*1600, {50,16}*1600, {10,80}*1600a, {80,10}*1600a, {80,10}*1600b, {20,40}*1600a, {20,20}*1600a, {20,20}*1600c, {20,40}*1600b, {20,40}*1600c, {40,20}*1600c, {40,20}*1600d, {20,40}*1600e, {40,20}*1600e, {40,20}*1600f, {10,80}*1600c, {25,4}*1600, {5,10}*1600, {5,20}*1600
81-fold covers : {405,2}*1620, {45,18}*1620, {45,6}*1620a, {135,6}*1620, {45,6}*1620b, {45,6}*1620c, {45,6}*1620d, {15,6}*1620, {15,18}*1620, {5,6}*1620
82-fold covers : {10,82}*1640, {410,2}*1640
83-fold covers : {415,2}*1660
84-fold covers : {60,14}*1680, {30,28}*1680a, {20,42}*1680a, {10,84}*1680, {70,12}*1680, {140,6}*1680a, {420,2}*1680, {210,4}*1680a, {105,6}*1680, {105,4}*1680
85-fold covers : {425,2}*1700, {85,10}*1700
86-fold covers : {10,86}*1720, {430,2}*1720
87-fold covers : {435,2}*1740
88-fold covers : {40,22}*1760, {10,88}*1760, {20,44}*1760, {220,4}*1760, {440,2}*1760, {110,8}*1760
89-fold covers : {445,2}*1780
90-fold covers : {50,18}*1800, {450,2}*1800, {150,6}*1800a, {150,6}*1800b, {150,6}*1800c, {10,90}*1800a, {10,90}*1800b, {90,10}*1800b, {90,10}*1800c, {30,30}*1800a, {30,30}*1800c, {30,30}*1800e, {30,30}*1800f, {30,30}*1800g, {30,30}*1800i
91-fold covers : {455,2}*1820
92-fold covers : {20,46}*1840, {10,92}*1840, {460,2}*1840, {230,4}*1840
93-fold covers : {465,2}*1860
94-fold covers : {10,94}*1880, {470,2}*1880
95-fold covers : {475,2}*1900, {95,10}*1900
96-fold covers : {60,8}*1920a, {120,4}*1920a, {40,12}*1920a, {20,24}*1920a, {120,8}*1920a, {120,8}*1920b, {120,8}*1920c, {40,24}*1920a, {40,24}*1920b, {40,24}*1920c, {120,8}*1920d, {40,24}*1920d, {60,16}*1920a, {240,4}*1920a, {80,12}*1920a, {20,48}*1920a, {60,16}*1920b, {240,4}*1920b, {80,12}*1920b, {20,48}*1920b, {60,4}*1920a, {120,4}*1920b, {60,8}*1920b, {40,12}*1920b, {20,24}*1920b, {20,12}*1920a, {30,32}*1920, {480,2}*1920, {10,96}*1920, {160,6}*1920, {15,12}*1920, {15,8}*1920a, {30,8}*1920a, {30,6}*1920a, {40,6}*1920a, {40,12}*1920e, {40,12}*1920f, {60,12}*1920a, {60,12}*1920b, {40,6}*1920b, {60,6}*1920, {20,6}*1920a, {30,6}*1920b, {30,6}*1920c, {40,6}*1920c, {20,24}*1920c, {20,24}*1920d, {40,6}*1920d, {120,6}*1920a, {20,6}*1920b, {120,6}*1920b, {20,12}*1920b, {20,12}*1920c, {60,12}*1920c, {30,24}*1920a, {30,12}*1920, {40,12}*1920g, {40,12}*1920h, {60,12}*1920d, {20,24}*1920e, {20,24}*1920f, {30,24}*1920b, {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {30,4}*1920a, {30,8}*1920d, {30,8}*1920e, {30,8}*1920f, {60,8}*1920g, {60,8}*1920h, {120,4}*1920c, {120,4}*1920d, {30,8}*1920g, {60,4}*1920e, {120,4}*1920e, {30,4}*1920b, {120,4}*1920f, {15,8}*1920b, {15,4}*1920a, {15,8}*1920c, {30,4}*1920c, {10,12}*1920a, {30,4}*1920d
97-fold covers : {485,2}*1940
98-fold covers : {10,98}*1960, {490,2}*1960, {70,14}*1960a, {70,14}*1960b, {70,14}*1960c
99-fold covers : {495,2}*1980, {165,6}*1980
100-fold covers : {500,2}*2000, {250,4}*2000, {20,50}*2000a, {50,20}*2000a, {10,100}*2000a, {100,10}*2000a, {100,10}*2000b, {10,20}*2000b, {20,10}*2000a, {20,10}*2000b, {50,20}*2000b, {10,20}*2000c, {10,20}*2000h, {20,10}*2000h, {10,4}*2000b, {20,4}*2000b, {20,10}*2000j
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(7)!(2,3)(4,5);
s1 := Sym(7)!(1,2)(3,4);
s2 := Sym(7)!(6,7);
poly := sub<Sym(7)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope