Polytope of Type {2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20}*80
if this polytope has a name.
Group : SmallGroup(80,37)
Rank : 3
Schlafli Type : {2,20}
Number of vertices, edges, etc : 2, 20, 20
Order of s0s1s2 : 20
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,20,2} of size 160
   {2,20,4} of size 320
   {2,20,6} of size 480
   {2,20,6} of size 480
   {2,20,4} of size 640
   {2,20,8} of size 640
   {2,20,8} of size 640
   {2,20,6} of size 720
   {2,20,10} of size 800
   {2,20,10} of size 800
   {2,20,10} of size 800
   {2,20,12} of size 960
   {2,20,6} of size 960
   {2,20,6} of size 960
   {2,20,10} of size 960
   {2,20,10} of size 960
   {2,20,3} of size 960
   {2,20,5} of size 960
   {2,20,6} of size 960
   {2,20,14} of size 1120
   {2,20,8} of size 1280
   {2,20,16} of size 1280
   {2,20,16} of size 1280
   {2,20,4} of size 1280
   {2,20,8} of size 1280
   {2,20,4} of size 1280
   {2,20,4} of size 1280
   {2,20,4} of size 1280
   {2,20,4} of size 1280
   {2,20,5} of size 1280
   {2,20,5} of size 1280
   {2,20,18} of size 1440
   {2,20,18} of size 1440
   {2,20,4} of size 1440
   {2,20,6} of size 1440
   {2,20,20} of size 1600
   {2,20,20} of size 1600
   {2,20,20} of size 1600
   {2,20,4} of size 1600
   {2,20,22} of size 1760
   {2,20,24} of size 1920
   {2,20,24} of size 1920
   {2,20,12} of size 1920
   {2,20,12} of size 1920
   {2,20,6} of size 1920
   {2,20,12} of size 1920
   {2,20,4} of size 1920
   {2,20,4} of size 1920
   {2,20,6} of size 1920
   {2,20,6} of size 1920
   {2,20,10} of size 1920
   {2,20,4} of size 1920
   {2,20,4} of size 1920
   {2,20,6} of size 1920
   {2,20,6} of size 1920
   {2,20,10} of size 1920
   {2,20,4} of size 2000
   {2,20,10} of size 2000
   {2,20,10} of size 2000
   {2,20,10} of size 2000
   {2,20,10} of size 2000
   {2,20,10} of size 2000
Vertex Figure Of :
   {2,2,20} of size 160
   {3,2,20} of size 240
   {4,2,20} of size 320
   {5,2,20} of size 400
   {6,2,20} of size 480
   {7,2,20} of size 560
   {8,2,20} of size 640
   {9,2,20} of size 720
   {10,2,20} of size 800
   {11,2,20} of size 880
   {12,2,20} of size 960
   {13,2,20} of size 1040
   {14,2,20} of size 1120
   {15,2,20} of size 1200
   {16,2,20} of size 1280
   {17,2,20} of size 1360
   {18,2,20} of size 1440
   {19,2,20} of size 1520
   {20,2,20} of size 1600
   {21,2,20} of size 1680
   {22,2,20} of size 1760
   {23,2,20} of size 1840
   {24,2,20} of size 1920
   {25,2,20} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,10}*40
   4-fold quotients : {2,5}*20
   5-fold quotients : {2,4}*16
   10-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,20}*160, {2,40}*160
   3-fold covers : {6,20}*240a, {2,60}*240
   4-fold covers : {4,40}*320a, {4,20}*320, {4,40}*320b, {8,20}*320a, {8,20}*320b, {2,80}*320
   5-fold covers : {2,100}*400, {10,20}*400a, {10,20}*400b
   6-fold covers : {6,40}*480, {12,20}*480, {4,60}*480a, {2,120}*480
   7-fold covers : {14,20}*560, {2,140}*560
   8-fold covers : {4,40}*640a, {8,40}*640a, {8,40}*640b, {8,20}*640a, {8,40}*640c, {8,40}*640d, {4,80}*640a, {4,80}*640b, {4,20}*640a, {4,40}*640b, {8,20}*640b, {16,20}*640a, {16,20}*640b, {2,160}*640
   9-fold covers : {18,20}*720a, {2,180}*720, {6,60}*720a, {6,60}*720b, {6,60}*720c, {6,20}*720
   10-fold covers : {4,100}*800, {2,200}*800, {10,40}*800a, {10,40}*800b, {20,20}*800a, {20,20}*800b
   11-fold covers : {22,20}*880, {2,220}*880
   12-fold covers : {6,80}*960, {12,20}*960a, {24,20}*960a, {12,40}*960a, {24,20}*960b, {12,40}*960b, {4,120}*960a, {4,60}*960a, {4,120}*960b, {8,60}*960a, {8,60}*960b, {2,240}*960, {6,20}*960e, {6,60}*960a, {4,60}*960b
   13-fold covers : {26,20}*1040, {2,260}*1040
   14-fold covers : {14,40}*1120, {28,20}*1120, {4,140}*1120, {2,280}*1120
   15-fold covers : {6,100}*1200a, {2,300}*1200, {30,20}*1200a, {30,20}*1200b, {10,60}*1200b, {10,60}*1200c
   16-fold covers : {8,40}*1280a, {8,20}*1280a, {8,40}*1280b, {4,40}*1280a, {8,40}*1280c, {8,40}*1280d, {16,20}*1280a, {4,80}*1280a, {16,20}*1280b, {4,80}*1280b, {8,80}*1280a, {16,40}*1280a, {8,80}*1280b, {16,40}*1280b, {16,40}*1280c, {8,80}*1280c, {8,80}*1280d, {16,40}*1280d, {16,40}*1280e, {8,80}*1280e, {8,80}*1280f, {16,40}*1280f, {32,20}*1280a, {4,160}*1280a, {32,20}*1280b, {4,160}*1280b, {4,20}*1280a, {4,40}*1280b, {8,20}*1280b, {8,20}*1280c, {8,40}*1280e, {4,40}*1280c, {4,40}*1280d, {8,20}*1280d, {8,40}*1280f, {8,40}*1280g, {8,40}*1280h, {2,320}*1280, {4,20}*1280c
   17-fold covers : {34,20}*1360, {2,340}*1360
   18-fold covers : {18,40}*1440, {36,20}*1440, {4,180}*1440a, {2,360}*1440, {6,120}*1440a, {12,60}*1440a, {6,120}*1440b, {6,120}*1440c, {12,60}*1440b, {12,60}*1440c, {4,20}*1440, {4,60}*1440, {6,40}*1440, {12,20}*1440
   19-fold covers : {38,20}*1520, {2,380}*1520
   20-fold covers : {4,200}*1600a, {4,100}*1600, {4,200}*1600b, {8,100}*1600a, {8,100}*1600b, {2,400}*1600, {10,80}*1600a, {10,80}*1600b, {40,20}*1600a, {20,20}*1600a, {20,20}*1600b, {40,20}*1600b, {20,40}*1600c, {20,40}*1600d, {40,20}*1600c, {20,40}*1600e, {20,40}*1600f, {40,20}*1600e
   21-fold covers : {14,60}*1680, {42,20}*1680a, {6,140}*1680a, {2,420}*1680
   22-fold covers : {22,40}*1760, {44,20}*1760, {4,220}*1760, {2,440}*1760
   23-fold covers : {46,20}*1840, {2,460}*1840
   24-fold covers : {8,60}*1920a, {4,120}*1920a, {12,40}*1920a, {24,20}*1920a, {8,120}*1920a, {8,120}*1920b, {8,120}*1920c, {24,40}*1920a, {24,40}*1920b, {24,40}*1920c, {8,120}*1920d, {24,40}*1920d, {16,60}*1920a, {4,240}*1920a, {12,80}*1920a, {48,20}*1920a, {16,60}*1920b, {4,240}*1920b, {12,80}*1920b, {48,20}*1920b, {4,60}*1920a, {4,120}*1920b, {8,60}*1920b, {12,40}*1920b, {24,20}*1920b, {12,20}*1920a, {2,480}*1920, {6,160}*1920, {12,60}*1920b, {6,40}*1920b, {6,60}*1920, {6,40}*1920d, {6,120}*1920a, {6,20}*1920b, {6,120}*1920b, {12,20}*1920b, {12,20}*1920c, {12,60}*1920c, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,120}*1920c, {4,120}*1920d
   25-fold covers : {2,500}*2000, {50,20}*2000a, {10,100}*2000a, {10,100}*2000b, {10,20}*2000a, {10,20}*2000b, {10,20}*2000h, {10,20}*2000j
Permutation Representation (GAP) : 
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,21)(14,18)(16,19)(20,22);;
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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(22)!(1,2);
s1 := Sym(22)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22);
s2 := Sym(22)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,21)(14,18)(16,19)
(20,22);
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

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