Polytope of Type {2,14,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,10}*560
if this polytope has a name.
Group : SmallGroup(560,176)
Rank : 4
Schlafli Type : {2,14,10}
Number of vertices, edges, etc : 2, 14, 70, 10
Order of s₀s₁s₂s₃ : 70
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,10,2} of size 1120
Vertex Figure Of :
   {2,2,14,10} of size 1120
   {3,2,14,10} of size 1680
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,14,2}*112
   7-fold quotients : {2,2,10}*80
   10-fold quotients : {2,7,2}*56
   14-fold quotients : {2,2,5}*40
   35-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,14,20}*1120, {2,28,10}*1120, {4,14,10}*1120
   3-fold covers : {6,14,10}*1680, {2,14,30}*1680, {2,42,10}*1680
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope