Polytope of Type {70,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {70,2,4}*1120
if this polytope has a name.
Group : SmallGroup(1120,1061)
Rank : 4
Schlafli Type : {70,2,4}
Number of vertices, edges, etc : 70, 70, 4, 4
Order of s₀s₁s₂s₃ : 140
Order of s₀s₁s₂s₃s₂s₁ : 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 : {35,2,4}*560, {70,2,2}*560
   4-fold quotients : {35,2,2}*280
   5-fold quotients : {14,2,4}*224
   7-fold quotients : {10,2,4}*160
   10-fold quotients : {7,2,4}*112, {14,2,2}*112
   14-fold quotients : {5,2,4}*80, {10,2,2}*80
   20-fold quotients : {7,2,2}*56
   28-fold quotients : {5,2,2}*40
   35-fold quotients : {2,2,4}*32
   70-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope