Polytope of Type {2,2,6,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,26}*1248
if this polytope has a name.
Group : SmallGroup(1248,1451)
Rank : 5
Schlafli Type : {2,2,6,26}
Number of vertices, edges, etc : 2, 2, 6, 78, 26
Order of s₀s₁s₂s₃s₄ : 78
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) :
   3-fold quotients : {2,2,2,26}*416
   6-fold quotients : {2,2,2,13}*208
   13-fold quotients : {2,2,6,2}*96
   26-fold quotients : {2,2,3,2}*48
   39-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (18,31)(19,32)(20,33)(21,34)(22,35)(23,36)(24,37)(25,38)(26,39)(27,40)
(28,41)(29,42)(30,43)(57,70)(58,71)(59,72)(60,73)(61,74)(62,75)(63,76)(64,77)
(65,78)(66,79)(67,80)(68,81)(69,82);;
s3 := ( 5,18)( 6,30)( 7,29)( 8,28)( 9,27)(10,26)(11,25)(12,24)(13,23)(14,22)
(15,21)(16,20)(17,19)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(44,57)(45,69)
(46,68)(47,67)(48,66)(49,65)(50,64)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58)
(71,82)(72,81)(73,80)(74,79)(75,78)(76,77);;
s4 := ( 5,45)( 6,44)( 7,56)( 8,55)( 9,54)(10,53)(11,52)(12,51)(13,50)(14,49)
(15,48)(16,47)(17,46)(18,58)(19,57)(20,69)(21,68)(22,67)(23,66)(24,65)(25,64)
(26,63)(27,62)(28,61)(29,60)(30,59)(31,71)(32,70)(33,82)(34,81)(35,80)(36,79)
(37,78)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72);;
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*s1*s0*s1, 
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(82)!(1,2);
s1 := Sym(82)!(3,4);
s2 := Sym(82)!(18,31)(19,32)(20,33)(21,34)(22,35)(23,36)(24,37)(25,38)(26,39)
(27,40)(28,41)(29,42)(30,43)(57,70)(58,71)(59,72)(60,73)(61,74)(62,75)(63,76)
(64,77)(65,78)(66,79)(67,80)(68,81)(69,82);
s3 := Sym(82)!( 5,18)( 6,30)( 7,29)( 8,28)( 9,27)(10,26)(11,25)(12,24)(13,23)
(14,22)(15,21)(16,20)(17,19)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(44,57)
(45,69)(46,68)(47,67)(48,66)(49,65)(50,64)(51,63)(52,62)(53,61)(54,60)(55,59)
(56,58)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77);
s4 := Sym(82)!( 5,45)( 6,44)( 7,56)( 8,55)( 9,54)(10,53)(11,52)(12,51)(13,50)
(14,49)(15,48)(16,47)(17,46)(18,58)(19,57)(20,69)(21,68)(22,67)(23,66)(24,65)
(25,64)(26,63)(27,62)(28,61)(29,60)(30,59)(31,71)(32,70)(33,82)(34,81)(35,80)
(36,79)(37,78)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72);
poly := sub<Sym(82)|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*s1*s0*s1, 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, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope