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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,4,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,134249)
Rank : 5
Schlafli Type : {2,18,4,4}
Number of vertices, edges, etc : 2, 18, 36, 8, 4
Order of s₀s₁s₂s₃s₄ : 36
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 : {2,18,2,4}*576, {2,18,4,2}*576a
   3-fold quotients : {2,6,4,4}*384
   4-fold quotients : {2,9,2,4}*288, {2,18,2,2}*288
   6-fold quotients : {2,6,2,4}*192, {2,6,4,2}*192a
   8-fold quotients : {2,9,2,2}*144
   9-fold quotients : {2,2,4,4}*128
   12-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
   18-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   24-fold quotients : {2,3,2,2}*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 := ( 4, 5)( 6,11)( 7,10)( 8, 9)(13,14)(15,20)(16,19)(17,18)(22,23)(24,29)
(25,28)(26,27)(31,32)(33,38)(34,37)(35,36)(40,41)(42,47)(43,46)(44,45)(49,50)
(51,56)(52,55)(53,54)(58,59)(60,65)(61,64)(62,63)(67,68)(69,74)(70,73)
(71,72);;
s2 := ( 3, 6)( 4, 8)( 5, 7)( 9,11)(12,15)(13,17)(14,16)(18,20)(21,24)(22,26)
(23,25)(27,29)(30,33)(31,35)(32,34)(36,38)(39,51)(40,53)(41,52)(42,48)(43,50)
(44,49)(45,56)(46,55)(47,54)(57,69)(58,71)(59,70)(60,66)(61,68)(62,67)(63,74)
(64,73)(65,72);;
s3 := ( 3,39)( 4,40)( 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)(23,59)
(24,60)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)(32,68)(33,69)(34,70)
(35,71)(36,72)(37,73)(38,74);;
s4 := (39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)
(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope