Polytope of Type {2,2,18,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,18,8}*1152
if this polytope has a name.
Group : SmallGroup(1152,152539)
Rank : 5
Schlafli Type : {2,2,18,8}
Number of vertices, edges, etc : 2, 2, 18, 72, 8
Order of s₀s₁s₂s₃s₄ : 72
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 : {2,2,18,4}*576a
   3-fold quotients : {2,2,6,8}*384
   4-fold quotients : {2,2,18,2}*288
   6-fold quotients : {2,2,6,4}*192a
   8-fold quotients : {2,2,9,2}*144
   9-fold quotients : {2,2,2,8}*128
   12-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,2,2,4}*64
   24-fold quotients : {2,2,3,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope