Questions?
See the FAQ
or other info.

Polytope of Type {2,28,4,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,4,2,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1076200)
Rank : 6
Schlafli Type : {2,28,4,2,2}
Number of vertices, edges, etc : 2, 28, 56, 4, 2, 2
Order of s0s1s2s3s4s5 : 28
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,28,2,2,2}*896, {2,14,4,2,2}*896
   4-fold quotients : {2,14,2,2,2}*448
   7-fold quotients : {2,4,4,2,2}*256
   8-fold quotients : {2,7,2,2,2}*224
   14-fold quotients : {2,2,4,2,2}*128, {2,4,2,2,2}*128
   28-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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)(31,45)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,52)(39,58)
(40,57)(41,56)(42,55)(43,54)(44,53);;
s2 := ( 3,32)( 4,31)( 5,37)( 6,36)( 7,35)( 8,34)( 9,33)(10,39)(11,38)(12,44)
(13,43)(14,42)(15,41)(16,40)(17,46)(18,45)(19,51)(20,50)(21,49)(22,48)(23,47)
(24,53)(25,52)(26,58)(27,57)(28,56)(29,55)(30,54);;
s3 := (31,38)(32,39)(33,40)(34,41)(35,42)(36,43)(37,44)(45,52)(46,53)(47,54)
(48,55)(49,56)(50,57)(51,58);;
s4 := (59,60);;
s5 := (61,62);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
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*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(62)!(1,2);
s1 := Sym(62)!( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)
(25,30)(26,29)(27,28)(31,45)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,52)
(39,58)(40,57)(41,56)(42,55)(43,54)(44,53);
s2 := Sym(62)!( 3,32)( 4,31)( 5,37)( 6,36)( 7,35)( 8,34)( 9,33)(10,39)(11,38)
(12,44)(13,43)(14,42)(15,41)(16,40)(17,46)(18,45)(19,51)(20,50)(21,49)(22,48)
(23,47)(24,53)(25,52)(26,58)(27,57)(28,56)(29,55)(30,54);
s3 := Sym(62)!(31,38)(32,39)(33,40)(34,41)(35,42)(36,43)(37,44)(45,52)(46,53)
(47,54)(48,55)(49,56)(50,57)(51,58);
s4 := Sym(62)!(59,60);
s5 := Sym(62)!(61,62);
poly := sub<Sym(62)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
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*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