Polytope of Type {2,28,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,4}*448
if this polytope has a name.
Group : SmallGroup(448,940)
Rank : 4
Schlafli Type : {2,28,4}
Number of vertices, edges, etc : 2, 28, 56, 4
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,28,4,2} of size 896
   {2,28,4,4} of size 1792
Vertex Figure Of :
   {2,2,28,4} of size 896
   {3,2,28,4} of size 1344
   {4,2,28,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,28,2}*224, {2,14,4}*224
   4-fold quotients : {2,14,2}*112
   7-fold quotients : {2,4,4}*64
   8-fold quotients : {2,7,2}*56
   14-fold quotients : {2,2,4}*32, {2,4,2}*32
   28-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,28,4}*896, {2,56,4}*896a, {2,28,4}*896, {2,56,4}*896b, {2,28,8}*896a, {2,28,8}*896b
   3-fold covers : {6,28,4}*1344, {2,28,12}*1344, {2,84,4}*1344a
   4-fold covers : {2,28,8}*1792a, {2,56,4}*1792a, {2,56,8}*1792a, {2,56,8}*1792b, {2,56,8}*1792c, {2,56,8}*1792d, {4,28,8}*1792a, {8,28,4}*1792a, {4,28,8}*1792b, {8,28,4}*1792b, {4,56,4}*1792a, {4,28,4}*1792a, {4,28,4}*1792b, {4,56,4}*1792b, {4,56,4}*1792c, {4,56,4}*1792d, {2,28,16}*1792a, {2,112,4}*1792a, {2,28,16}*1792b, {2,112,4}*1792b, {2,28,4}*1792, {2,56,4}*1792b, {2,28,8}*1792b
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);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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(58)!(1,2);
s1 := Sym(58)!( 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(58)!( 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(58)!(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);
poly := sub<Sym(58)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, 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