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Polytope of Type {8,2,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,28}*896
if this polytope has a name.
Group : SmallGroup(896,11816)
Rank : 4
Schlafli Type : {8,2,28}
Number of vertices, edges, etc : 8, 8, 28, 28
Order of s0s1s2s3 : 56
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,28,2} of size 1792
Vertex Figure Of :
   {2,8,2,28} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,28}*448, {8,2,14}*448
   4-fold quotients : {8,2,7}*224, {2,2,28}*224, {4,2,14}*224
   7-fold quotients : {8,2,4}*128
   8-fold quotients : {4,2,7}*112, {2,2,14}*112
   14-fold quotients : {4,2,4}*64, {8,2,2}*64
   16-fold quotients : {2,2,7}*56
   28-fold quotients : {2,2,4}*32, {4,2,2}*32
   56-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,56}*1792, {8,4,28}*1792a, {16,2,28}*1792
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11)(12,13)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28)(29,30)
(31,34)(32,33)(35,36);;
s3 := ( 9,15)(10,12)(11,21)(13,23)(14,17)(16,19)(18,29)(20,31)(22,25)(24,27)
(26,35)(28,32)(30,33)(34,36);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(36)!(2,3)(4,5)(6,7);
s1 := Sym(36)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(36)!(10,11)(12,13)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28)
(29,30)(31,34)(32,33)(35,36);
s3 := Sym(36)!( 9,15)(10,12)(11,21)(13,23)(14,17)(16,19)(18,29)(20,31)(22,25)
(24,27)(26,35)(28,32)(30,33)(34,36);
poly := sub<Sym(36)|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 >; 
 

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