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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,10,14}*1680
if this polytope has a name.
Group : SmallGroup(1680,966)
Rank : 5
Schlafli Type : {3,2,10,14}
Number of vertices, edges, etc : 3, 3, 10, 70, 14
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 : {3,2,2,14}*336
   7-fold quotients : {3,2,10,2}*240
   10-fold quotients : {3,2,2,7}*168
   14-fold quotients : {3,2,5,2}*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 := (11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,25)(19,26)(20,27)
(21,28)(22,29)(23,30)(24,31)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)
(53,60)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66);;
s3 := ( 4,11)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(18,32)(19,38)(20,37)
(21,36)(22,35)(23,34)(24,33)(26,31)(27,30)(28,29)(39,46)(40,52)(41,51)(42,50)
(43,49)(44,48)(45,47)(53,67)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(61,66)
(62,65)(63,64);;
s4 := ( 4,40)( 5,39)( 6,45)( 7,44)( 8,43)( 9,42)(10,41)(11,47)(12,46)(13,52)
(14,51)(15,50)(16,49)(17,48)(18,54)(19,53)(20,59)(21,58)(22,57)(23,56)(24,55)
(25,61)(26,60)(27,66)(28,65)(29,64)(30,63)(31,62)(32,68)(33,67)(34,73)(35,72)
(36,71)(37,70)(38,69);;
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, 
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(73)!(2,3);
s1 := Sym(73)!(1,2);
s2 := Sym(73)!(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,25)(19,26)
(20,27)(21,28)(22,29)(23,30)(24,31)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)
(52,73)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66);
s3 := Sym(73)!( 4,11)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(18,32)(19,38)
(20,37)(21,36)(22,35)(23,34)(24,33)(26,31)(27,30)(28,29)(39,46)(40,52)(41,51)
(42,50)(43,49)(44,48)(45,47)(53,67)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)
(61,66)(62,65)(63,64);
s4 := Sym(73)!( 4,40)( 5,39)( 6,45)( 7,44)( 8,43)( 9,42)(10,41)(11,47)(12,46)
(13,52)(14,51)(15,50)(16,49)(17,48)(18,54)(19,53)(20,59)(21,58)(22,57)(23,56)
(24,55)(25,61)(26,60)(27,66)(28,65)(29,64)(30,63)(31,62)(32,68)(33,67)(34,73)
(35,72)(36,71)(37,70)(38,69);
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, 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