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Polytope of Type {20,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,2}*80
if this polytope has a name.
Group : SmallGroup(80,37)
Rank : 3
Schlafli Type : {20,2}
Number of vertices, edges, etc : 20, 20, 2
Order of s0s1s2 : 20
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {20,2,2} of size 160
   {20,2,3} of size 240
   {20,2,4} of size 320
   {20,2,5} of size 400
   {20,2,6} of size 480
   {20,2,7} of size 560
   {20,2,8} of size 640
   {20,2,9} of size 720
   {20,2,10} of size 800
   {20,2,11} of size 880
   {20,2,12} of size 960
   {20,2,13} of size 1040
   {20,2,14} of size 1120
   {20,2,15} of size 1200
   {20,2,16} of size 1280
   {20,2,17} of size 1360
   {20,2,18} of size 1440
   {20,2,19} of size 1520
   {20,2,20} of size 1600
   {20,2,21} of size 1680
   {20,2,22} of size 1760
   {20,2,23} of size 1840
   {20,2,24} of size 1920
   {20,2,25} of size 2000
Vertex Figure Of :
   {2,20,2} of size 160
   {4,20,2} of size 320
   {6,20,2} of size 480
   {6,20,2} of size 480
   {4,20,2} of size 640
   {8,20,2} of size 640
   {8,20,2} of size 640
   {6,20,2} of size 720
   {10,20,2} of size 800
   {10,20,2} of size 800
   {10,20,2} of size 800
   {12,20,2} of size 960
   {6,20,2} of size 960
   {6,20,2} of size 960
   {10,20,2} of size 960
   {10,20,2} of size 960
   {3,20,2} of size 960
   {5,20,2} of size 960
   {6,20,2} of size 960
   {14,20,2} of size 1120
   {8,20,2} of size 1280
   {16,20,2} of size 1280
   {16,20,2} of size 1280
   {4,20,2} of size 1280
   {8,20,2} of size 1280
   {4,20,2} of size 1280
   {4,20,2} of size 1280
   {4,20,2} of size 1280
   {4,20,2} of size 1280
   {5,20,2} of size 1280
   {5,20,2} of size 1280
   {18,20,2} of size 1440
   {18,20,2} of size 1440
   {4,20,2} of size 1440
   {6,20,2} of size 1440
   {20,20,2} of size 1600
   {20,20,2} of size 1600
   {20,20,2} of size 1600
   {4,20,2} of size 1600
   {22,20,2} of size 1760
   {24,20,2} of size 1920
   {24,20,2} of size 1920
   {12,20,2} of size 1920
   {12,20,2} of size 1920
   {6,20,2} of size 1920
   {12,20,2} of size 1920
   {4,20,2} of size 1920
   {4,20,2} of size 1920
   {6,20,2} of size 1920
   {6,20,2} of size 1920
   {10,20,2} of size 1920
   {4,20,2} of size 1920
   {4,20,2} of size 1920
   {6,20,2} of size 1920
   {6,20,2} of size 1920
   {10,20,2} of size 1920
   {4,20,2} of size 2000
   {10,20,2} of size 2000
   {10,20,2} of size 2000
   {10,20,2} of size 2000
   {10,20,2} of size 2000
   {10,20,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,2}*40
   4-fold quotients : {5,2}*20
   5-fold quotients : {4,2}*16
   10-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,4}*160, {40,2}*160
   3-fold covers : {20,6}*240a, {60,2}*240
   4-fold covers : {40,4}*320a, {20,4}*320, {40,4}*320b, {20,8}*320a, {20,8}*320b, {80,2}*320
   5-fold covers : {100,2}*400, {20,10}*400a, {20,10}*400b
   6-fold covers : {40,6}*480, {20,12}*480, {60,4}*480a, {120,2}*480
   7-fold covers : {20,14}*560, {140,2}*560
   8-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
   9-fold covers : {20,18}*720a, {180,2}*720, {60,6}*720a, {60,6}*720b, {60,6}*720c, {20,6}*720
   10-fold covers : {100,4}*800, {200,2}*800, {40,10}*800a, {40,10}*800b, {20,20}*800a, {20,20}*800c
   11-fold covers : {20,22}*880, {220,2}*880
   12-fold covers : {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, {20,6}*960e, {60,6}*960a, {60,4}*960b
   13-fold covers : {20,26}*1040, {260,2}*1040
   14-fold covers : {40,14}*1120, {20,28}*1120, {140,4}*1120, {280,2}*1120
   15-fold covers : {100,6}*1200a, {300,2}*1200, {20,30}*1200a, {20,30}*1200b, {60,10}*1200b, {60,10}*1200c
   16-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, {320,2}*1280, {20,4}*1280c
   17-fold covers : {20,34}*1360, {340,2}*1360
   18-fold covers : {40,18}*1440, {20,36}*1440, {180,4}*1440a, {360,2}*1440, {120,6}*1440a, {60,12}*1440a, {120,6}*1440b, {120,6}*1440c, {60,12}*1440b, {60,12}*1440c, {20,4}*1440, {60,4}*1440, {40,6}*1440, {20,12}*1440
   19-fold covers : {20,38}*1520, {380,2}*1520
   20-fold covers : {200,4}*1600a, {100,4}*1600, {200,4}*1600b, {100,8}*1600a, {100,8}*1600b, {400,2}*1600, {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
   21-fold covers : {60,14}*1680, {20,42}*1680a, {140,6}*1680a, {420,2}*1680
   22-fold covers : {40,22}*1760, {20,44}*1760, {220,4}*1760, {440,2}*1760
   23-fold covers : {20,46}*1840, {460,2}*1840
   24-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, {480,2}*1920, {160,6}*1920, {60,12}*1920b, {40,6}*1920b, {60,6}*1920, {40,6}*1920d, {120,6}*1920a, {20,6}*1920b, {120,6}*1920b, {20,12}*1920b, {20,12}*1920c, {60,12}*1920c, {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {120,4}*1920c, {120,4}*1920d
   25-fold covers : {500,2}*2000, {20,50}*2000a, {100,10}*2000a, {100,10}*2000b, {20,10}*2000a, {20,10}*2000b, {20,10}*2000h, {20,10}*2000j
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)(18,20);;
s2 := (21,22);;
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*s0*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*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(22)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);
s1 := Sym(22)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)
(18,20);
s2 := Sym(22)!(21,22);
poly := sub<Sym(22)|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*s0*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*s0*s1*s0*s1 >; 
 

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