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Polytope of Type {2,12,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,134264)
Rank : 5
Schlafli Type : {2,12,4,6}
Number of vertices, edges, etc : 2, 12, 24, 12, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,2,6}*576, {2,6,4,6}*576
   3-fold quotients : {2,12,4,2}*384a, {2,4,4,6}*384
   4-fold quotients : {2,12,2,3}*288, {2,6,2,6}*288
   6-fold quotients : {2,12,2,2}*192, {2,2,4,6}*192a, {2,4,2,6}*192, {2,6,4,2}*192a
   8-fold quotients : {2,3,2,6}*144, {2,6,2,3}*144
   9-fold quotients : {2,4,4,2}*128
   12-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96, {2,6,2,2}*96
   16-fold quotients : {2,3,2,3}*72
   18-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   24-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)
(34,37)(35,38)(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);;
s2 := ( 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)(21,60)(22,61)(23,62)
(24,57)(25,58)(26,59)(27,63)(28,64)(29,65)(30,69)(31,70)(32,71)(33,66)(34,67)
(35,68)(36,72)(37,73)(38,74);;
s3 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(46,56)(47,55)
(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73);;
s4 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)
(66,67)(69,70)(72,73);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)
(33,36)(34,37)(35,38)(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);
s2 := 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)(21,60)(22,61)
(23,62)(24,57)(25,58)(26,59)(27,63)(28,64)(29,65)(30,69)(31,70)(32,71)(33,66)
(34,67)(35,68)(36,72)(37,73)(38,74);
s3 := 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)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(46,56)
(47,55)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73);
s4 := Sym(74)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)
(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)
(63,64)(66,67)(69,70)(72,73);
poly := sub<Sym(74)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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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