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Polytope of Type {2,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,4}*320
if this polytope has a name.
Group : SmallGroup(320,1159)
Rank : 4
Schlafli Type : {2,20,4}
Number of vertices, edges, etc : 2, 20, 40, 4
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,20,4,2} of size 640
   {2,20,4,4} of size 1280
   {2,20,4,6} of size 1920
   {2,20,4,3} of size 1920
Vertex Figure Of :
   {2,2,20,4} of size 640
   {3,2,20,4} of size 960
   {4,2,20,4} of size 1280
   {5,2,20,4} of size 1600
   {6,2,20,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,20,2}*160, {2,10,4}*160
   4-fold quotients : {2,10,2}*80
   5-fold quotients : {2,4,4}*64
   8-fold quotients : {2,5,2}*40
   10-fold quotients : {2,2,4}*32, {2,4,2}*32
   20-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,20,4}*640, {2,40,4}*640a, {2,20,4}*640, {2,40,4}*640b, {2,20,8}*640a, {2,20,8}*640b
   3-fold covers : {6,20,4}*960, {2,20,12}*960, {2,60,4}*960a
   4-fold covers : {2,20,8}*1280a, {2,40,4}*1280a, {2,40,8}*1280a, {2,40,8}*1280b, {2,40,8}*1280c, {2,40,8}*1280d, {4,20,8}*1280a, {8,20,4}*1280a, {4,20,8}*1280b, {8,20,4}*1280b, {4,40,4}*1280a, {4,20,4}*1280a, {4,20,4}*1280b, {4,40,4}*1280b, {4,40,4}*1280c, {4,40,4}*1280d, {2,20,16}*1280a, {2,80,4}*1280a, {2,20,16}*1280b, {2,80,4}*1280b, {2,20,4}*1280a, {2,40,4}*1280b, {2,20,8}*1280b
   5-fold covers : {2,100,4}*1600, {10,20,4}*1600a, {10,20,4}*1600b, {2,20,20}*1600a, {2,20,20}*1600c
   6-fold covers : {4,60,4}*1920a, {4,20,12}*1920, {12,20,4}*1920, {2,60,8}*1920a, {2,120,4}*1920a, {6,20,8}*1920a, {6,40,4}*1920a, {2,40,12}*1920a, {2,20,24}*1920a, {2,60,8}*1920b, {2,120,4}*1920b, {6,20,8}*1920b, {6,40,4}*1920b, {2,40,12}*1920b, {2,20,24}*1920b, {2,60,4}*1920a, {6,20,4}*1920a, {2,20,12}*1920a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(23,33)(24,37)
(25,36)(26,35)(27,34)(28,38)(29,42)(30,41)(31,40)(32,39)(44,47)(45,46)(49,52)
(50,51)(54,57)(55,56)(59,62)(60,61)(63,73)(64,77)(65,76)(66,75)(67,74)(68,78)
(69,82)(70,81)(71,80)(72,79);;
s2 := ( 3,24)( 4,23)( 5,27)( 6,26)( 7,25)( 8,29)( 9,28)(10,32)(11,31)(12,30)
(13,34)(14,33)(15,37)(16,36)(17,35)(18,39)(19,38)(20,42)(21,41)(22,40)(43,64)
(44,63)(45,67)(46,66)(47,65)(48,69)(49,68)(50,72)(51,71)(52,70)(53,74)(54,73)
(55,77)(56,76)(57,75)(58,79)(59,78)(60,82)(61,81)(62,80);;
s3 := ( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)
(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,68)
(24,69)(25,70)(26,71)(27,72)(28,63)(29,64)(30,65)(31,66)(32,67)(33,78)(34,79)
(35,80)(36,81)(37,82)(38,73)(39,74)(40,75)(41,76)(42,77);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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(82)!(1,2);
s1 := Sym(82)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(23,33)
(24,37)(25,36)(26,35)(27,34)(28,38)(29,42)(30,41)(31,40)(32,39)(44,47)(45,46)
(49,52)(50,51)(54,57)(55,56)(59,62)(60,61)(63,73)(64,77)(65,76)(66,75)(67,74)
(68,78)(69,82)(70,81)(71,80)(72,79);
s2 := Sym(82)!( 3,24)( 4,23)( 5,27)( 6,26)( 7,25)( 8,29)( 9,28)(10,32)(11,31)
(12,30)(13,34)(14,33)(15,37)(16,36)(17,35)(18,39)(19,38)(20,42)(21,41)(22,40)
(43,64)(44,63)(45,67)(46,66)(47,65)(48,69)(49,68)(50,72)(51,71)(52,70)(53,74)
(54,73)(55,77)(56,76)(57,75)(58,79)(59,78)(60,82)(61,81)(62,80);
s3 := Sym(82)!( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)
(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)
(23,68)(24,69)(25,70)(26,71)(27,72)(28,63)(29,64)(30,65)(31,66)(32,67)(33,78)
(34,79)(35,80)(36,81)(37,82)(38,73)(39,74)(40,75)(41,76)(42,77);
poly := sub<Sym(82)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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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