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Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*576a
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 12, 72, 24
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,12,2} of size 1152
Vertex Figure Of :
   {2,2,6,12} of size 1152
   {3,2,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,12}*288d
   3-fold quotients : {2,6,4}*192
   4-fold quotients : {2,6,6}*144a
   6-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   12-fold quotients : {2,3,4}*48, {2,2,6}*48, {2,6,2}*48
   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 : {2,12,12}*1152d, {2,6,12}*1152b, {4,6,12}*1152b, {2,6,24}*1152c, {2,6,24}*1152e, {2,12,12}*1152j
   3-fold covers : {2,6,36}*1728, {2,18,12}*1728a, {2,6,12}*1728b, {6,6,12}*1728a, {6,6,12}*1728b, {2,6,12}*1728c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 8, 9)(12,13)(15,27)(16,29)(17,28)(18,30)(19,31)(20,33)(21,32)
(22,34)(23,35)(24,37)(25,36)(26,38)(40,41)(44,45)(48,49)(51,63)(52,65)(53,64)
(54,66)(55,67)(56,69)(57,68)(58,70)(59,71)(60,73)(61,72)(62,74);;
s2 := ( 3,15)( 4,16)( 5,18)( 6,17)( 7,23)( 8,24)( 9,26)(10,25)(11,19)(12,20)
(13,22)(14,21)(29,30)(31,35)(32,36)(33,38)(34,37)(39,51)(40,52)(41,54)(42,53)
(43,59)(44,60)(45,62)(46,61)(47,55)(48,56)(49,58)(50,57)(65,66)(67,71)(68,72)
(69,74)(70,73);;
s3 := ( 3,46)( 4,45)( 5,44)( 6,43)( 7,42)( 8,41)( 9,40)(10,39)(11,50)(12,49)
(13,48)(14,47)(15,58)(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,62)
(24,61)(25,60)(26,59)(27,70)(28,69)(29,68)(30,67)(31,66)(32,65)(33,64)(34,63)
(35,74)(36,73)(37,72)(38,71);;
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*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 4, 5)( 8, 9)(12,13)(15,27)(16,29)(17,28)(18,30)(19,31)(20,33)
(21,32)(22,34)(23,35)(24,37)(25,36)(26,38)(40,41)(44,45)(48,49)(51,63)(52,65)
(53,64)(54,66)(55,67)(56,69)(57,68)(58,70)(59,71)(60,73)(61,72)(62,74);
s2 := Sym(74)!( 3,15)( 4,16)( 5,18)( 6,17)( 7,23)( 8,24)( 9,26)(10,25)(11,19)
(12,20)(13,22)(14,21)(29,30)(31,35)(32,36)(33,38)(34,37)(39,51)(40,52)(41,54)
(42,53)(43,59)(44,60)(45,62)(46,61)(47,55)(48,56)(49,58)(50,57)(65,66)(67,71)
(68,72)(69,74)(70,73);
s3 := Sym(74)!( 3,46)( 4,45)( 5,44)( 6,43)( 7,42)( 8,41)( 9,40)(10,39)(11,50)
(12,49)(13,48)(14,47)(15,58)(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)
(23,62)(24,61)(25,60)(26,59)(27,70)(28,69)(29,68)(30,67)(31,66)(32,65)(33,64)
(34,63)(35,74)(36,73)(37,72)(38,71);
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*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >; 
 

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