Polytope of Type {7,2,4,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,4,4,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,336970)
Rank : 6
Schlafli Type : {7,2,4,4,4}
Number of vertices, edges, etc : 7, 7, 4, 8, 8, 4
Order of s₀s₁s₂s₃s₄s₅ : 28
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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 : {7,2,2,4,4}*896, {7,2,4,4,2}*896, {7,2,4,2,4}*896
   4-fold quotients : {7,2,2,2,4}*448, {7,2,2,4,2}*448, {7,2,4,2,2}*448
   8-fold quotients : {7,2,2,2,2}*224
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 8,16)( 9,17)(10,18)(11,19)(12,20)(13,21)(14,22)(15,23)(24,32)(25,33)
(26,34)(27,35)(28,36)(29,37)(30,38)(31,39)(40,48)(41,49)(42,50)(43,51)(44,52)
(45,53)(46,54)(47,55)(56,64)(57,65)(58,66)(59,67)(60,68)(61,69)(62,70)
(63,71);;
s3 := (16,20)(17,21)(18,22)(19,23)(24,26)(25,27)(28,30)(29,31)(32,38)(33,39)
(34,36)(35,37)(40,44)(41,45)(42,46)(43,47)(56,62)(57,63)(58,60)(59,61)(64,66)
(65,67)(68,70)(69,71);;
s4 := ( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(17,33)
(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(40,56)(41,57)(42,58)(43,59)(44,60)
(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)(52,68)(53,69)(54,70)
(55,71);;
s5 := ( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,40)(17,41)
(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,65)(25,64)(26,67)(27,66)(28,69)
(29,68)(30,71)(31,70)(32,57)(33,56)(34,59)(35,58)(36,61)(37,60)(38,63)
(39,62);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(71)!(2,3)(4,5)(6,7);
s1 := Sym(71)!(1,2)(3,4)(5,6);
s2 := Sym(71)!( 8,16)( 9,17)(10,18)(11,19)(12,20)(13,21)(14,22)(15,23)(24,32)
(25,33)(26,34)(27,35)(28,36)(29,37)(30,38)(31,39)(40,48)(41,49)(42,50)(43,51)
(44,52)(45,53)(46,54)(47,55)(56,64)(57,65)(58,66)(59,67)(60,68)(61,69)(62,70)
(63,71);
s3 := Sym(71)!(16,20)(17,21)(18,22)(19,23)(24,26)(25,27)(28,30)(29,31)(32,38)
(33,39)(34,36)(35,37)(40,44)(41,45)(42,46)(43,47)(56,62)(57,63)(58,60)(59,61)
(64,66)(65,67)(68,70)(69,71);
s4 := Sym(71)!( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)
(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(40,56)(41,57)(42,58)(43,59)
(44,60)(45,61)(46,62)(47,63)(48,64)(49,65)(50,66)(51,67)(52,68)(53,69)(54,70)
(55,71);
s5 := Sym(71)!( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,40)
(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,65)(25,64)(26,67)(27,66)
(28,69)(29,68)(30,71)(31,70)(32,57)(33,56)(34,59)(35,58)(36,61)(37,60)(38,63)
(39,62);
poly := sub<Sym(71)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope