Polytope of Type {2,2,10,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,14}*1120
if this polytope has a name.
Group : SmallGroup(1120,1088)
Rank : 5
Schlafli Type : {2,2,10,14}
Number of vertices, edges, etc : 2, 2, 10, 70, 14
Order of s₀s₁s₂s₃s₄ : 70
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) :
   5-fold quotients : {2,2,2,14}*224
   7-fold quotients : {2,2,10,2}*160
   10-fold quotients : {2,2,2,7}*112
   14-fold quotients : {2,2,5,2}*80
   35-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope