Polytope of Type {7,2,16,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,16,4}*1792a
if this polytope has a name.
Group : SmallGroup(1792,323301)
Rank : 5
Schlafli Type : {7,2,16,4}
Number of vertices, edges, etc : 7, 7, 16, 32, 4
Order of s₀s₁s₂s₃s₄ : 112
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 : {7,2,8,4}*896a, {7,2,16,2}*896
   4-fold quotients : {7,2,4,4}*448, {7,2,8,2}*448
   8-fold quotients : {7,2,2,4}*224, {7,2,4,2}*224
   16-fold quotients : {7,2,2,2}*112
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 := ( 8,40)( 9,41)(10,43)(11,42)(12,44)(13,45)(14,47)(15,46)(16,50)(17,51)
(18,48)(19,49)(20,54)(21,55)(22,52)(23,53)(24,56)(25,57)(26,59)(27,58)(28,60)
(29,61)(30,63)(31,62)(32,66)(33,67)(34,64)(35,65)(36,70)(37,71)(38,68)
(39,69);;
s3 := (10,11)(14,15)(16,18)(17,19)(20,22)(21,23)(24,28)(25,29)(26,31)(27,30)
(32,38)(33,39)(34,36)(35,37)(40,48)(41,49)(42,51)(43,50)(44,52)(45,53)(46,55)
(47,54)(56,68)(57,69)(58,71)(59,70)(60,64)(61,65)(62,67)(63,66);;
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);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(71)!(2,3)(4,5)(6,7);
s1 := Sym(71)!(1,2)(3,4)(5,6);
s2 := Sym(71)!( 8,40)( 9,41)(10,43)(11,42)(12,44)(13,45)(14,47)(15,46)(16,50)
(17,51)(18,48)(19,49)(20,54)(21,55)(22,52)(23,53)(24,56)(25,57)(26,59)(27,58)
(28,60)(29,61)(30,63)(31,62)(32,66)(33,67)(34,64)(35,65)(36,70)(37,71)(38,68)
(39,69);
s3 := Sym(71)!(10,11)(14,15)(16,18)(17,19)(20,22)(21,23)(24,28)(25,29)(26,31)
(27,30)(32,38)(33,39)(34,36)(35,37)(40,48)(41,49)(42,51)(43,50)(44,52)(45,53)
(46,55)(47,54)(56,68)(57,69)(58,71)(59,70)(60,64)(61,65)(62,67)(63,66);
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);
poly := sub<Sym(71)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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