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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,6,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,136369)
Rank : 5
Schlafli Type : {4,2,6,4}
Number of vertices, edges, etc : 4, 4, 18, 36, 12
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,6,4}*576, {2,2,6,4}*576
   4-fold quotients : {2,2,6,4}*288
   9-fold quotients : {4,2,2,4}*128
   18-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope