Polytope of Type {2,26,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,6}*624
if this polytope has a name.
Group : SmallGroup(624,251)
Rank : 4
Schlafli Type : {2,26,6}
Number of vertices, edges, etc : 2, 26, 78, 6
Order of s₀s₁s₂s₃ : 78
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,26,6,2} of size 1248
   {2,26,6,3} of size 1872
Vertex Figure Of :
   {2,2,26,6} of size 1248
   {3,2,26,6} of size 1872
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,26,2}*208
   6-fold quotients : {2,13,2}*104
   13-fold quotients : {2,2,6}*48
   26-fold quotients : {2,2,3}*24
   39-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,26,12}*1248, {2,52,6}*1248a, {4,26,6}*1248
   3-fold covers : {2,26,18}*1872, {6,26,6}*1872, {2,78,6}*1872a, {2,78,6}*1872b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope