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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,6}*576d
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 5
Schlafli Type : {2,4,6,6}
Number of vertices, edges, etc : 2, 4, 12, 18, 6
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,6,6,2} of size 1152
   {2,4,6,6,3} of size 1728
Vertex Figure Of :
   {2,2,4,6,6} of size 1152
   {3,2,4,6,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,4,6,2}*192c
   6-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,12,6}*1152d, {2,4,12,6}*1152f, {2,4,6,12}*1152d, {2,4,6,6}*1152a
   3-fold covers : {2,4,6,18}*1728c, {2,4,18,6}*1728c, {2,4,6,6}*1728e, {2,4,6,6}*1728i
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope