Polytope of Type {5,2,18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,18,4}*1440c
if this polytope has a name.
Group : SmallGroup(1440,4569)
Rank : 5
Schlafli Type : {5,2,18,4}
Number of vertices, edges, etc : 5, 5, 18, 36, 4
Order of s₀s₁s₂s₃s₄ : 45
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {5,2,9,4}*720
   3-fold quotients : {5,2,6,4}*480b
   6-fold quotients : {5,2,3,4}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)(10,14)(11,16)(12,15)(13,17)(18,34)(19,36)(20,35)(21,37)(22,30)
(23,32)(24,31)(25,33)(26,38)(27,40)(28,39)(29,41)(43,44)(46,50)(47,52)(48,51)
(49,53)(54,70)(55,72)(56,71)(57,73)(58,66)(59,68)(60,67)(61,69)(62,74)(63,76)
(64,75)(65,77);;
s3 := ( 6,54)( 7,55)( 8,57)( 9,56)(10,62)(11,63)(12,65)(13,64)(14,58)(15,59)
(16,61)(17,60)(18,42)(19,43)(20,45)(21,44)(22,50)(23,51)(24,53)(25,52)(26,46)
(27,47)(28,49)(29,48)(30,70)(31,71)(32,73)(33,72)(34,66)(35,67)(36,69)(37,68)
(38,74)(39,75)(40,77)(41,76);;
s4 := ( 6,45)( 7,44)( 8,43)( 9,42)(10,49)(11,48)(12,47)(13,46)(14,53)(15,52)
(16,51)(17,50)(18,57)(19,56)(20,55)(21,54)(22,61)(23,60)(24,59)(25,58)(26,65)
(27,64)(28,63)(29,62)(30,69)(31,68)(32,67)(33,66)(34,73)(35,72)(36,71)(37,70)
(38,77)(39,76)(40,75)(41,74);;
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*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, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s2*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(77)!(2,3)(4,5);
s1 := Sym(77)!(1,2)(3,4);
s2 := Sym(77)!( 7, 8)(10,14)(11,16)(12,15)(13,17)(18,34)(19,36)(20,35)(21,37)
(22,30)(23,32)(24,31)(25,33)(26,38)(27,40)(28,39)(29,41)(43,44)(46,50)(47,52)
(48,51)(49,53)(54,70)(55,72)(56,71)(57,73)(58,66)(59,68)(60,67)(61,69)(62,74)
(63,76)(64,75)(65,77);
s3 := Sym(77)!( 6,54)( 7,55)( 8,57)( 9,56)(10,62)(11,63)(12,65)(13,64)(14,58)
(15,59)(16,61)(17,60)(18,42)(19,43)(20,45)(21,44)(22,50)(23,51)(24,53)(25,52)
(26,46)(27,47)(28,49)(29,48)(30,70)(31,71)(32,73)(33,72)(34,66)(35,67)(36,69)
(37,68)(38,74)(39,75)(40,77)(41,76);
s4 := Sym(77)!( 6,45)( 7,44)( 8,43)( 9,42)(10,49)(11,48)(12,47)(13,46)(14,53)
(15,52)(16,51)(17,50)(18,57)(19,56)(20,55)(21,54)(22,61)(23,60)(24,59)(25,58)
(26,65)(27,64)(28,63)(29,62)(30,69)(31,68)(32,67)(33,66)(34,73)(35,72)(36,71)
(37,70)(38,77)(39,76)(40,75)(41,74);
poly := sub<Sym(77)|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, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s2*s4 >;

to this polytope