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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}*576a
if this polytope has a name.
Group : SmallGroup(576,6554)
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}*288a
   3-fold quotients : {2,2,24}*192, {2,6,8}*192
   4-fold quotients : {2,6,6}*144a
   6-fold quotients : {2,2,12}*96, {2,6,4}*96a
   9-fold quotients : {2,2,8}*64
   12-fold quotients : {2,2,6}*48, {2,6,2}*48
   18-fold quotients : {2,2,4}*32
   24-fold quotients : {2,2,3}*24, {2,3,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,24}*1152a, {4,6,24}*1152b, {2,6,48}*1152b
   3-fold covers : {2,6,72}*1728a, {2,18,24}*1728a, {2,6,24}*1728b, {6,6,24}*1728b, {6,6,24}*1728d, {2,6,24}*1728f
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74);;
s2 := ( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,31)(22,30)
(23,32)(24,37)(25,36)(26,38)(27,34)(28,33)(29,35)(39,58)(40,57)(41,59)(42,64)
(43,63)(44,65)(45,61)(46,60)(47,62)(48,67)(49,66)(50,68)(51,73)(52,72)(53,74)
(54,70)(55,69)(56,71);;
s3 := ( 3,42)( 4,43)( 5,44)( 6,39)( 7,40)( 8,41)( 9,45)(10,46)(11,47)(12,51)
(13,52)(14,53)(15,48)(16,49)(17,50)(18,54)(19,55)(20,56)(21,69)(22,70)(23,71)
(24,66)(25,67)(26,68)(27,72)(28,73)(29,74)(30,60)(31,61)(32,62)(33,57)(34,58)
(35,59)(36,63)(37,64)(38,65);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)
(64,65)(67,68)(70,71)(73,74);
s2 := Sym(74)!( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,31)
(22,30)(23,32)(24,37)(25,36)(26,38)(27,34)(28,33)(29,35)(39,58)(40,57)(41,59)
(42,64)(43,63)(44,65)(45,61)(46,60)(47,62)(48,67)(49,66)(50,68)(51,73)(52,72)
(53,74)(54,70)(55,69)(56,71);
s3 := Sym(74)!( 3,42)( 4,43)( 5,44)( 6,39)( 7,40)( 8,41)( 9,45)(10,46)(11,47)
(12,51)(13,52)(14,53)(15,48)(16,49)(17,50)(18,54)(19,55)(20,56)(21,69)(22,70)
(23,71)(24,66)(25,67)(26,68)(27,72)(28,73)(29,74)(30,60)(31,61)(32,62)(33,57)
(34,58)(35,59)(36,63)(37,64)(38,65);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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