Polytope of Type {2,2,4,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,36}*1152a
if this polytope has a name.
Group : SmallGroup(1152,134258)
Rank : 5
Schlafli Type : {2,2,4,36}
Number of vertices, edges, etc : 2, 2, 4, 72, 36
Order of s₀s₁s₂s₃s₄ : 36
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) :
   2-fold quotients : {2,2,2,36}*576, {2,2,4,18}*576a
   3-fold quotients : {2,2,4,12}*384a
   4-fold quotients : {2,2,2,18}*288
   6-fold quotients : {2,2,2,12}*192, {2,2,4,6}*192a
   8-fold quotients : {2,2,2,9}*144
   9-fold quotients : {2,2,4,4}*128
   12-fold quotients : {2,2,2,6}*96
   18-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   24-fold quotients : {2,2,2,3}*48
   36-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 := (41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(48,57)(49,58)(59,68)
(60,69)(61,70)(62,71)(63,72)(64,73)(65,74)(66,75)(67,76);;
s3 := ( 5,41)( 6,43)( 7,42)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)(14,50)
(15,52)(16,51)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,59)(24,61)(25,60)
(26,66)(27,65)(28,67)(29,63)(30,62)(31,64)(32,68)(33,70)(34,69)(35,75)(36,74)
(37,76)(38,72)(39,71)(40,73);;
s4 := ( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,26)(24,28)
(25,27)(29,30)(32,35)(33,37)(34,36)(38,39)(41,62)(42,64)(43,63)(44,59)(45,61)
(46,60)(47,66)(48,65)(49,67)(50,71)(51,73)(52,72)(53,68)(54,70)(55,69)(56,75)
(57,74)(58,76);;
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*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*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*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(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(48,57)(49,58)
(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74)(66,75)(67,76);
s3 := Sym(76)!( 5,41)( 6,43)( 7,42)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)
(14,50)(15,52)(16,51)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,59)(24,61)
(25,60)(26,66)(27,65)(28,67)(29,63)(30,62)(31,64)(32,68)(33,70)(34,69)(35,75)
(36,74)(37,76)(38,72)(39,71)(40,73);
s4 := Sym(76)!( 5, 8)( 6,10)( 7, 9)(11,12)(14,17)(15,19)(16,18)(20,21)(23,26)
(24,28)(25,27)(29,30)(32,35)(33,37)(34,36)(38,39)(41,62)(42,64)(43,63)(44,59)
(45,61)(46,60)(47,66)(48,65)(49,67)(50,71)(51,73)(52,72)(53,68)(54,70)(55,69)
(56,75)(57,74)(58,76);
poly := sub<Sym(76)|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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope