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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,26,6}*1248
if this polytope has a name.
Group : SmallGroup(1248,1451)
Rank : 5
Schlafli Type : {2,2,26,6}
Number of vertices, edges, etc : 2, 2, 26, 78, 6
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 : {2,2,26,2}*416
   6-fold quotients : {2,2,13,2}*208
   13-fold quotients : {2,2,2,6}*96
   26-fold quotients : {2,2,2,3}*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 := ( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(11,12)(19,30)(20,29)(21,28)(22,27)
(23,26)(24,25)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(45,56)(46,55)(47,54)
(48,53)(49,52)(50,51)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,82)(72,81)
(73,80)(74,79)(75,78)(76,77);;
s3 := ( 5, 6)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(18,32)(19,31)(20,43)(21,42)
(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(44,45)(46,56)
(47,55)(48,54)(49,53)(50,52)(57,71)(58,70)(59,82)(60,81)(61,80)(62,79)(63,78)
(64,77)(65,76)(66,75)(67,74)(68,73)(69,72);;
s4 := ( 5,57)( 6,58)( 7,59)( 8,60)( 9,61)(10,62)(11,63)(12,64)(13,65)(14,66)
(15,67)(16,68)(17,69)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)
(26,52)(27,53)(28,54)(29,55)(30,56)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)
(37,76)(38,77)(39,78)(40,79)(41,80)(42,81)(43,82);;
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, 
s3*s4*s3*s4*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope