Polytope of Type {2,4,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,26}*416
if this polytope has a name.
Group : SmallGroup(416,216)
Rank : 4
Schlafli Type : {2,4,26}
Number of vertices, edges, etc : 2, 4, 52, 26
Order of s₀s₁s₂s₃ : 52
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,26,2} of size 832
   {2,4,26,4} of size 1664
Vertex Figure Of :
   {2,2,4,26} of size 832
   {3,2,4,26} of size 1248
   {4,2,4,26} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,26}*208
   4-fold quotients : {2,2,13}*104
   13-fold quotients : {2,4,2}*32
   26-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,52}*832, {4,4,26}*832, {2,8,26}*832
   3-fold covers : {2,12,26}*1248, {6,4,26}*1248, {2,4,78}*1248a
   4-fold covers : {4,4,52}*1664, {4,8,26}*1664a, {8,4,26}*1664a, {2,8,52}*1664a, {2,4,104}*1664a, {4,8,26}*1664b, {8,4,26}*1664b, {2,8,52}*1664b, {2,4,104}*1664b, {4,4,26}*1664, {2,4,52}*1664, {2,16,26}*1664
Permutation Representation (GAP) :

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