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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,18}*1152
if this polytope has a name.
Group : SmallGroup(1152,134249)
Rank : 5
Schlafli Type : {2,4,4,18}
Number of vertices, edges, etc : 2, 4, 8, 36, 18
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 : {2,2,4,18}*576a, {2,4,2,18}*576
   3-fold quotients : {2,4,4,6}*384
   4-fold quotients : {2,4,2,9}*288, {2,2,2,18}*288
   6-fold quotients : {2,2,4,6}*192a, {2,4,2,6}*192
   8-fold quotients : {2,2,2,9}*144
   9-fold quotients : {2,4,4,2}*128
   12-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
   18-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   24-fold quotients : {2,2,2,3}*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 := (39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(57,66)
(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);;
s2 := ( 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);;
s3 := ( 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)(39,57)(40,59)(41,58)(42,65)(43,64)
(44,63)(45,62)(46,61)(47,60)(48,66)(49,68)(50,67)(51,74)(52,73)(53,72)(54,71)
(55,70)(56,69);;
s4 := ( 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)(39,42)(40,44)(41,43)(45,47)(48,51)
(49,53)(50,52)(54,56)(57,60)(58,62)(59,61)(63,65)(66,69)(67,71)(68,70)
(72,74);;
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, 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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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)!(39,48)(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)
(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74);
s2 := 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);
s3 := 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)(39,57)(40,59)(41,58)(42,65)
(43,64)(44,63)(45,62)(46,61)(47,60)(48,66)(49,68)(50,67)(51,74)(52,73)(53,72)
(54,71)(55,70)(56,69);
s4 := 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)(39,42)(40,44)(41,43)(45,47)
(48,51)(49,53)(50,52)(54,56)(57,60)(58,62)(59,61)(63,65)(66,69)(67,71)(68,70)
(72,74);
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, 
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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope