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Polytope of Type {2,36,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,36,4}*576a
if this polytope has a name.
Group : SmallGroup(576,1471)
Rank : 4
Schlafli Type : {2,36,4}
Number of vertices, edges, etc : 2, 36, 72, 4
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,36,4,2} of size 1152
Vertex Figure Of :
   {2,2,36,4} of size 1152
   {3,2,36,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,36,2}*288, {2,18,4}*288a
   3-fold quotients : {2,12,4}*192a
   4-fold quotients : {2,18,2}*144
   6-fold quotients : {2,12,2}*96, {2,6,4}*96a
   8-fold quotients : {2,9,2}*72
   9-fold quotients : {2,4,4}*64
   12-fold quotients : {2,6,2}*48
   18-fold quotients : {2,2,4}*32, {2,4,2}*32
   24-fold quotients : {2,3,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,36,4}*1152a, {2,36,8}*1152a, {2,72,4}*1152a, {2,36,8}*1152b, {2,72,4}*1152b, {2,36,4}*1152a
   3-fold covers : {2,108,4}*1728a, {6,36,4}*1728a, {6,36,4}*1728b, {2,36,12}*1728a, {2,36,12}*1728b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6,10)( 7, 9)( 8,11)(13,14)(15,19)(16,18)(17,20)(22,23)(24,28)
(25,27)(26,29)(31,32)(33,37)(34,36)(35,38)(39,57)(40,59)(41,58)(42,64)(43,63)
(44,65)(45,61)(46,60)(47,62)(48,66)(49,68)(50,67)(51,73)(52,72)(53,74)(54,70)
(55,69)(56,71);;
s2 := ( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,46)(10,45)(11,47)(12,51)
(13,53)(14,52)(15,48)(16,50)(17,49)(18,55)(19,54)(20,56)(21,60)(22,62)(23,61)
(24,57)(25,59)(26,58)(27,64)(28,63)(29,65)(30,69)(31,71)(32,70)(33,66)(34,68)
(35,67)(36,73)(37,72)(38,74);;
s3 := (39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(57,66)
(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);;
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*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(74)!(1,2);
s1 := Sym(74)!( 4, 5)( 6,10)( 7, 9)( 8,11)(13,14)(15,19)(16,18)(17,20)(22,23)
(24,28)(25,27)(26,29)(31,32)(33,37)(34,36)(35,38)(39,57)(40,59)(41,58)(42,64)
(43,63)(44,65)(45,61)(46,60)(47,62)(48,66)(49,68)(50,67)(51,73)(52,72)(53,74)
(54,70)(55,69)(56,71);
s2 := Sym(74)!( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,46)(10,45)(11,47)
(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,55)(19,54)(20,56)(21,60)(22,62)
(23,61)(24,57)(25,59)(26,58)(27,64)(28,63)(29,65)(30,69)(31,71)(32,70)(33,66)
(34,68)(35,67)(36,73)(37,72)(38,74);
s3 := Sym(74)!(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)
(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);
poly := sub<Sym(74)|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*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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