Polytope of Type {3,2,14,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,14,10}*1680
if this polytope has a name.
Group : SmallGroup(1680,966)
Rank : 5
Schlafli Type : {3,2,14,10}
Number of vertices, edges, etc : 3, 3, 14, 70, 10
Order of s₀s₁s₂s₃s₄ : 210
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 : {3,2,14,2}*336
   7-fold quotients : {3,2,2,10}*240
   10-fold quotients : {3,2,7,2}*168
   14-fold quotients : {3,2,2,5}*120
   35-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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