Polytope of Type {2,6,26}

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

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

to this polytope