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Polytope of Type {40,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,2,7}*1120
if this polytope has a name.
Group : SmallGroup(1120,302)
Rank : 4
Schlafli Type : {40,2,7}
Number of vertices, edges, etc : 40, 40, 7, 7
Order of s0s1s2s3 : 280
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 : {20,2,7}*560
4-fold quotients : {10,2,7}*280
5-fold quotients : {8,2,7}*224
8-fold quotients : {5,2,7}*140
10-fold quotients : {4,2,7}*112
20-fold quotients : {2,2,7}*56
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)
(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);;
s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)(14,20)
(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);;
s2 := (42,43)(44,45)(46,47);;
s3 := (41,42)(43,44)(45,46);;
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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(47)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)
(17,23)(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);
s1 := Sym(47)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)
(14,20)(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);
s2 := Sym(47)!(42,43)(44,45)(46,47);
s3 := Sym(47)!(41,42)(43,44)(45,46);
poly := sub<Sym(47)|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*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 >;

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