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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,28,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,364865)
Rank : 5
Schlafli Type : {4,2,28,4}
Number of vertices, edges, etc : 4, 4, 28, 56, 4
Order of s₀s₁s₂s₃s₄ : 28
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,2,28,4}*896, {4,2,28,2}*896, {4,2,14,4}*896
   4-fold quotients : {2,2,28,2}*448, {2,2,14,4}*448, {4,2,14,2}*448
   7-fold quotients : {4,2,4,4}*256
   8-fold quotients : {4,2,7,2}*224, {2,2,14,2}*224
   14-fold quotients : {2,2,4,4}*128, {4,2,2,4}*128, {4,2,4,2}*128
   16-fold quotients : {2,2,7,2}*112
   28-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64, {4,2,2,2}*64
   56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)
(28,31)(29,30)(33,47)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,54)(41,60)
(42,59)(43,58)(44,57)(45,56)(46,55);;
s3 := ( 5,34)( 6,33)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,41)(13,40)(14,46)
(15,45)(16,44)(17,43)(18,42)(19,48)(20,47)(21,53)(22,52)(23,51)(24,50)(25,49)
(26,55)(27,54)(28,60)(29,59)(30,58)(31,57)(32,56);;
s4 := (33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(47,54)(48,55)(49,56)
(50,57)(51,58)(52,59)(53,60);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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(60)!(2,3);
s1 := Sym(60)!(1,2)(3,4);
s2 := Sym(60)!( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)
(27,32)(28,31)(29,30)(33,47)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,54)
(41,60)(42,59)(43,58)(44,57)(45,56)(46,55);
s3 := Sym(60)!( 5,34)( 6,33)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,41)(13,40)
(14,46)(15,45)(16,44)(17,43)(18,42)(19,48)(20,47)(21,53)(22,52)(23,51)(24,50)
(25,49)(26,55)(27,54)(28,60)(29,59)(30,58)(31,57)(32,56);
s4 := Sym(60)!(33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(47,54)(48,55)
(49,56)(50,57)(51,58)(52,59)(53,60);
poly := sub<Sym(60)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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 >;

to this polytope