Polytope of Type {8,2,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,42}*1344
if this polytope has a name.
Group : SmallGroup(1344,11133)
Rank : 4
Schlafli Type : {8,2,42}
Number of vertices, edges, etc : 8, 8, 42, 42
Order of s₀s₁s₂s₃ : 168
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 : {8,2,21}*672, {4,2,42}*672
   3-fold quotients : {8,2,14}*448
   4-fold quotients : {4,2,21}*336, {2,2,42}*336
   6-fold quotients : {8,2,7}*224, {4,2,14}*224
   7-fold quotients : {8,2,6}*192
   8-fold quotients : {2,2,21}*168
   12-fold quotients : {4,2,7}*112, {2,2,14}*112
   14-fold quotients : {8,2,3}*96, {4,2,6}*96
   21-fold quotients : {8,2,2}*64
   24-fold quotients : {2,2,7}*56
   28-fold quotients : {4,2,3}*48, {2,2,6}*48
   42-fold quotients : {4,2,2}*32
   56-fold quotients : {2,2,3}*24
   84-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(15,16)(17,18)(19,22)(20,21)(23,24)(25,28)(26,27)(29,30)
(31,34)(32,33)(35,36)(37,40)(38,39)(41,42)(43,46)(44,45)(47,50)(48,49);;
s3 := ( 9,25)(10,19)(11,17)(12,27)(13,15)(14,37)(16,21)(18,31)(20,29)(22,39)
(23,26)(24,47)(28,33)(30,43)(32,41)(34,49)(35,38)(36,48)(40,45)(42,44)
(46,50);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*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(50)!(2,3)(4,5)(6,7);
s1 := Sym(50)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(50)!(11,12)(13,14)(15,16)(17,18)(19,22)(20,21)(23,24)(25,28)(26,27)
(29,30)(31,34)(32,33)(35,36)(37,40)(38,39)(41,42)(43,46)(44,45)(47,50)(48,49);
s3 := Sym(50)!( 9,25)(10,19)(11,17)(12,27)(13,15)(14,37)(16,21)(18,31)(20,29)
(22,39)(23,26)(24,47)(28,33)(30,43)(32,41)(34,49)(35,38)(36,48)(40,45)(42,44)
(46,50);
poly := sub<Sym(50)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*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 >;

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