Polytope of Type {2,4,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,18}*288c
if this polytope has a name.
Group : SmallGroup(288,835)
Rank : 4
Schlafli Type : {2,4,18}
Number of vertices, edges, etc : 2, 4, 36, 18
Order of s₀s₁s₂s₃ : 18
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,18,2} of size 576
   {2,4,18,4} of size 1152
   {2,4,18,4} of size 1152
   {2,4,18,6} of size 1728
Vertex Figure Of :
   {2,2,4,18} of size 576
   {3,2,4,18} of size 864
   {4,2,4,18} of size 1152
   {5,2,4,18} of size 1440
   {6,2,4,18} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,9}*144
   3-fold quotients : {2,4,6}*96b
   6-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,18}*576
   3-fold covers : {2,4,54}*864c, {2,12,18}*864c
   4-fold covers : {4,4,18}*1152c, {2,8,18}*1152a, {2,4,36}*1152b, {4,4,18}*1152d, {2,4,18}*1152b, {2,4,36}*1152c, {2,8,18}*1152b, {2,8,18}*1152c
   5-fold covers : {2,20,18}*1440b, {2,4,90}*1440c
   6-fold covers : {2,4,54}*1728, {6,4,18}*1728b, {2,12,18}*1728a, {2,12,18}*1728b
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s1*s2*s1 >;

to this polytope