Polytope of Type {4,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,28}*1008
if this polytope has a name.
Group : SmallGroup(1008,896)
Rank : 3
Schlafli Type : {4,28}
Number of vertices, edges, etc : 18, 252, 126
Order of s₀s₁s₂ : 42
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {4,4}*144
   14-fold quotients : {4,4}*72
   18-fold quotients : {2,14}*56
   36-fold quotients : {2,7}*28
   126-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope