Polytope of Type {4,4,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2,3}*864
if this polytope has a name.
Group : SmallGroup(864,4686)
Rank : 5
Schlafli Type : {4,4,2,3}
Number of vertices, edges, etc : 18, 36, 18, 3, 3
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,2,3,2} of size 1728
Vertex Figure Of :
   {2,4,4,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,2,3}*432
   18-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,2,3}*1728, {4,4,2,6}*1728
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope