Polytope of Type {10,14,2}

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

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