Polytope of Type {6,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,12}*576
Also Known As : {{6,4|2},{4,12|2}}. if this polytope has another name.
Group : SmallGroup(576,6139)
Rank : 4
Schlafli Type : {6,4,12}
Number of vertices, edges, etc : 6, 12, 24, 12
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,4,12,2} of size 1152
Vertex Figure Of :
   {2,6,4,12} of size 1152
   {3,6,4,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,12}*288, {6,4,6}*288
   3-fold quotients : {2,4,12}*192a, {6,4,4}*192
   4-fold quotients : {3,2,12}*144, {6,2,6}*144
   6-fold quotients : {2,2,12}*96, {2,4,6}*96a, {6,2,4}*96, {6,4,2}*96a
   8-fold quotients : {3,2,6}*72, {6,2,3}*72
   9-fold quotients : {2,4,4}*64
   12-fold quotients : {3,2,4}*48, {2,2,6}*48, {6,2,2}*48
   16-fold quotients : {3,2,3}*36
   18-fold quotients : {2,2,4}*32, {2,4,2}*32
   24-fold quotients : {2,2,3}*24, {3,2,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4,12}*1152, {6,8,12}*1152a, {6,4,24}*1152a, {6,8,12}*1152b, {6,4,24}*1152b, {6,4,12}*1152a
   3-fold covers : {18,4,12}*1728, {6,4,36}*1728, {6,12,12}*1728a, {6,12,12}*1728b, {6,12,12}*1728c, {6,12,12}*1728g
Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)
(65,66)(68,69)(71,72);;
s1 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)
(55,65)(56,64)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72);;
s2 := ( 1,37)( 2,38)( 3,39)( 4,43)( 5,44)( 6,45)( 7,40)( 8,41)( 9,42)(10,46)
(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,55)(20,56)(21,57)
(22,61)(23,62)(24,63)(25,58)(26,59)(27,60)(28,64)(29,65)(30,66)(31,70)(32,71)
(33,72)(34,67)(35,68)(36,69);;
s3 := ( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)
(29,32)(30,33)(37,58)(38,59)(39,60)(40,55)(41,56)(42,57)(43,61)(44,62)(45,63)
(46,67)(47,68)(48,69)(49,64)(50,65)(51,66)(52,70)(53,71)(54,72);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(72)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)
(62,63)(65,66)(68,69)(71,72);
s1 := Sym(72)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)
(28,29)(31,32)(34,35)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)
(45,54)(55,65)(56,64)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72);
s2 := Sym(72)!( 1,37)( 2,38)( 3,39)( 4,43)( 5,44)( 6,45)( 7,40)( 8,41)( 9,42)
(10,46)(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,55)(20,56)
(21,57)(22,61)(23,62)(24,63)(25,58)(26,59)(27,60)(28,64)(29,65)(30,66)(31,70)
(32,71)(33,72)(34,67)(35,68)(36,69);
s3 := Sym(72)!( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)
(28,31)(29,32)(30,33)(37,58)(38,59)(39,60)(40,55)(41,56)(42,57)(43,61)(44,62)
(45,63)(46,67)(47,68)(48,69)(49,64)(50,65)(51,66)(52,70)(53,71)(54,72);
poly := sub<Sym(72)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References : None.
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