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Polytope of Type {2,6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,24}*576c
if this polytope has a name.
Group : SmallGroup(576,6980)
Rank : 4
Schlafli Type : {2,6,24}
Number of vertices, edges, etc : 2, 6, 72, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,24,2} of size 1152
Vertex Figure Of :
   {2,2,6,24} of size 1152
   {3,2,6,24} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,12}*288c
   3-fold quotients : {2,6,8}*192
   4-fold quotients : {2,6,6}*144c
   6-fold quotients : {2,6,4}*96a
   8-fold quotients : {2,3,6}*72
   9-fold quotients : {2,2,8}*64
   12-fold quotients : {2,6,2}*48
   18-fold quotients : {2,2,4}*32
   24-fold quotients : {2,3,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,24}*1152c, {4,6,24}*1152a, {2,6,48}*1152a
   3-fold covers : {2,18,24}*1728b, {2,6,24}*1728c, {2,6,24}*1728f, {6,6,24}*1728f, {6,6,24}*1728g
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(22,23)(24,27)
(25,29)(26,28)(31,32)(33,36)(34,38)(35,37)(40,41)(42,45)(43,47)(44,46)(49,50)
(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)
(71,73);;
s2 := ( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)(12,52)
(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,70)(22,69)(23,71)
(24,67)(25,66)(26,68)(27,73)(28,72)(29,74)(30,61)(31,60)(32,62)(33,58)(34,57)
(35,59)(36,64)(37,63)(38,65);;
s3 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)
(25,37)(26,38)(27,33)(28,34)(29,35)(39,57)(40,58)(41,59)(42,63)(43,64)(44,65)
(45,60)(46,61)(47,62)(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)(55,70)
(56,71);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(22,23)
(24,27)(25,29)(26,28)(31,32)(33,36)(34,38)(35,37)(40,41)(42,45)(43,47)(44,46)
(49,50)(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)
(71,73);
s2 := Sym(74)!( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)
(12,52)(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,70)(22,69)
(23,71)(24,67)(25,66)(26,68)(27,73)(28,72)(29,74)(30,61)(31,60)(32,62)(33,58)
(34,57)(35,59)(36,64)(37,63)(38,65);
s3 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)
(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(39,57)(40,58)(41,59)(42,63)(43,64)
(44,65)(45,60)(46,61)(47,62)(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)
(55,70)(56,71);
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >; 
 

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