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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,4}*576
if this polytope has a name.
Group : SmallGroup(576,8666)
Rank : 5
Schlafli Type : {2,2,4,4}
Number of vertices, edges, etc : 2, 2, 18, 36, 18
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,4,2} of size 1152
Vertex Figure Of :
   {2,2,2,4,4} of size 1152
   {3,2,2,4,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,4,4}*288
   18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,4,4}*1152, {2,4,4,4}*1152b, {4,2,4,4}*1152
   3-fold covers : {2,2,4,12}*1728a, {2,2,12,4}*1728a, {2,2,4,12}*1728b, {2,2,12,4}*1728b, {2,6,4,4}*1728b, {6,2,4,4}*1728
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)
(36,39)(37,40)(41,50)(42,51)(43,52)(44,56)(45,57)(46,58)(47,53)(48,54)(49,55)
(59,68)(60,69)(61,70)(62,74)(63,75)(64,76)(65,71)(66,72)(67,73);;
s3 := ( 5,41)( 6,44)( 7,47)( 8,42)( 9,45)(10,48)(11,43)(12,46)(13,49)(14,50)
(15,53)(16,56)(17,51)(18,54)(19,57)(20,52)(21,55)(22,58)(23,59)(24,62)(25,65)
(26,60)(27,63)(28,66)(29,61)(30,64)(31,67)(32,68)(33,71)(34,74)(35,69)(36,72)
(37,75)(38,70)(39,73)(40,76);;
s4 := ( 5,33)( 6,32)( 7,34)( 8,36)( 9,35)(10,37)(11,39)(12,38)(13,40)(14,24)
(15,23)(16,25)(17,27)(18,26)(19,28)(20,30)(21,29)(22,31)(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)
(55,73)(56,75)(57,74)(58,76);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)
(35,38)(36,39)(37,40)(41,50)(42,51)(43,52)(44,56)(45,57)(46,58)(47,53)(48,54)
(49,55)(59,68)(60,69)(61,70)(62,74)(63,75)(64,76)(65,71)(66,72)(67,73);
s3 := Sym(76)!( 5,41)( 6,44)( 7,47)( 8,42)( 9,45)(10,48)(11,43)(12,46)(13,49)
(14,50)(15,53)(16,56)(17,51)(18,54)(19,57)(20,52)(21,55)(22,58)(23,59)(24,62)
(25,65)(26,60)(27,63)(28,66)(29,61)(30,64)(31,67)(32,68)(33,71)(34,74)(35,69)
(36,72)(37,75)(38,70)(39,73)(40,76);
s4 := Sym(76)!( 5,33)( 6,32)( 7,34)( 8,36)( 9,35)(10,37)(11,39)(12,38)(13,40)
(14,24)(15,23)(16,25)(17,27)(18,26)(19,28)(20,30)(21,29)(22,31)(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)(55,73)(56,75)(57,74)(58,76);
poly := sub<Sym(76)|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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 >;

to this polytope