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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,4,4,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,134249)
Rank : 5
Schlafli Type : {18,4,4,2}
Number of vertices, edges, etc : 18, 36, 8, 4, 2
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 : {18,2,4,2}*576, {18,4,2,2}*576a
   3-fold quotients : {6,4,4,2}*384
   4-fold quotients : {9,2,4,2}*288, {18,2,2,2}*288
   6-fold quotients : {6,2,4,2}*192, {6,4,2,2}*192a
   8-fold quotients : {9,2,2,2}*144
   9-fold quotients : {2,4,4,2}*128
   12-fold quotients : {3,2,4,2}*96, {6,2,2,2}*96
   18-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   24-fold quotients : {3,2,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope