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

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

to this polytope