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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,18,4}*576b
if this polytope has a name.
Group : SmallGroup(576,8262)
Rank : 5
Schlafli Type : {2,2,18,4}
Number of vertices, edges, etc : 2, 2, 18, 36, 4
Order of s₀s₁s₂s₃s₄ : 18
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,18,4,2} of size 1152
Vertex Figure Of :
   {2,2,2,18,4} of size 1152
   {3,2,2,18,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,9,4}*288
   3-fold quotients : {2,2,6,4}*192c
   6-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,36,4}*1152b, {2,2,36,4}*1152c, {2,4,18,4}*1152b, {4,2,18,4}*1152b, {2,2,18,4}*1152
   3-fold covers : {2,2,54,4}*1728b, {2,6,18,4}*1728c, {2,6,18,4}*1728d, {6,2,18,4}*1728b
Permutation Representation (GAP) :

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

to this polytope