Polytope of Type {4,4,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6,3}*576
if this polytope has a name.
Group : SmallGroup(576,7160)
Rank : 5
Schlafli Type : {4,4,6,3}
Number of vertices, edges, etc : 4, 8, 12, 9, 3
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,6,3,2} of size 1152
Vertex Figure Of :
   {2,4,4,6,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,6,3}*288, {2,4,6,3}*288
   3-fold quotients : {4,4,2,3}*192
   4-fold quotients : {2,2,6,3}*144
   6-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96
   12-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4,6,3}*1152a, {4,8,6,3}*1152a, {8,4,6,3}*1152b, {4,8,6,3}*1152b, {4,4,6,3}*1152, {4,4,6,6}*1152c
   3-fold covers : {4,4,6,9}*1728, {4,4,6,3}*1728a, {12,4,6,3}*1728, {4,12,6,3}*1728d
Permutation Representation (GAP) :

s0 := (37,46)(38,47)(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(55,64)
(56,65)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72);;
s1 := ( 1,37)( 2,38)( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)
(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)
(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)(32,68)
(33,69)(34,70)(35,71)(36,72);;
s2 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(37,55)(38,57)(39,56)(40,58)(41,60)(42,59)(43,61)(44,63)(45,62)
(46,64)(47,66)(48,65)(49,67)(50,69)(51,68)(52,70)(53,72)(54,71);;
s3 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,20)(22,26)
(23,25)(24,27)(28,29)(31,35)(32,34)(33,36)(37,38)(40,44)(41,43)(42,45)(46,47)
(49,53)(50,52)(51,54)(55,56)(58,62)(59,61)(60,63)(64,65)(67,71)(68,70)
(69,72);;
s4 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,13)(11,15)(12,14)(17,18)(19,22)(20,24)
(21,23)(26,27)(28,31)(29,33)(30,32)(35,36)(37,40)(38,42)(39,41)(44,45)(46,49)
(47,51)(48,50)(53,54)(55,58)(56,60)(57,59)(62,63)(64,67)(65,69)(66,68)
(71,72);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(72)!(37,46)(38,47)(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)
(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72);
s1 := Sym(72)!( 1,37)( 2,38)( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)
(10,46)(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)
(21,57)(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)
(32,68)(33,69)(34,70)(35,71)(36,72);
s2 := 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)(37,55)(38,57)(39,56)(40,58)(41,60)(42,59)(43,61)(44,63)
(45,62)(46,64)(47,66)(48,65)(49,67)(50,69)(51,68)(52,70)(53,72)(54,71);
s3 := Sym(72)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,20)
(22,26)(23,25)(24,27)(28,29)(31,35)(32,34)(33,36)(37,38)(40,44)(41,43)(42,45)
(46,47)(49,53)(50,52)(51,54)(55,56)(58,62)(59,61)(60,63)(64,65)(67,71)(68,70)
(69,72);
s4 := Sym(72)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,13)(11,15)(12,14)(17,18)(19,22)
(20,24)(21,23)(26,27)(28,31)(29,33)(30,32)(35,36)(37,40)(38,42)(39,41)(44,45)
(46,49)(47,51)(48,50)(53,54)(55,58)(56,60)(57,59)(62,63)(64,67)(65,69)(66,68)
(71,72);
poly := sub<Sym(72)|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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 >;

References : None.
to this polytope