Polytope of Type {2,6,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,36}*1296a
if this polytope has a name.
Group : SmallGroup(1296,2976)
Rank : 4
Schlafli Type : {2,6,36}
Number of vertices, edges, etc : 2, 9, 162, 54
Order of s₀s₁s₂s₃ : 36
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,6,12}*432c
   9-fold quotients : {2,6,4}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(30,57)
(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,75)(40,76)(41,77)
(42,78)(43,79)(44,80)(45,81)(46,82)(47,83)(48,66)(49,67)(50,68)(51,69)(52,70)
(53,71)(54,72)(55,73)(56,74);;
s2 := ( 3,30)( 4,32)( 5,31)( 6,38)( 7,37)( 8,36)( 9,35)(10,34)(11,33)(13,14)
(15,20)(16,19)(17,18)(21,75)(22,77)(23,76)(24,83)(25,82)(26,81)(27,80)(28,79)
(29,78)(39,66)(40,68)(41,67)(42,74)(43,73)(44,72)(45,71)(46,70)(47,69)(49,50)
(51,56)(52,55)(53,54)(58,59)(60,65)(61,64)(62,63);;
s3 := ( 3, 6)( 4, 8)( 5, 7)( 9,11)(12,24)(13,26)(14,25)(15,21)(16,23)(17,22)
(18,29)(19,28)(20,27)(30,42)(31,44)(32,43)(33,39)(34,41)(35,40)(36,47)(37,46)
(38,45)(48,51)(49,53)(50,52)(54,56)(57,78)(58,80)(59,79)(60,75)(61,77)(62,76)
(63,83)(64,82)(65,81)(66,69)(67,71)(68,70)(72,74);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*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(83)!(1,2);
s1 := Sym(83)!(12,21)(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)
(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,75)(40,76)
(41,77)(42,78)(43,79)(44,80)(45,81)(46,82)(47,83)(48,66)(49,67)(50,68)(51,69)
(52,70)(53,71)(54,72)(55,73)(56,74);
s2 := Sym(83)!( 3,30)( 4,32)( 5,31)( 6,38)( 7,37)( 8,36)( 9,35)(10,34)(11,33)
(13,14)(15,20)(16,19)(17,18)(21,75)(22,77)(23,76)(24,83)(25,82)(26,81)(27,80)
(28,79)(29,78)(39,66)(40,68)(41,67)(42,74)(43,73)(44,72)(45,71)(46,70)(47,69)
(49,50)(51,56)(52,55)(53,54)(58,59)(60,65)(61,64)(62,63);
s3 := Sym(83)!( 3, 6)( 4, 8)( 5, 7)( 9,11)(12,24)(13,26)(14,25)(15,21)(16,23)
(17,22)(18,29)(19,28)(20,27)(30,42)(31,44)(32,43)(33,39)(34,41)(35,40)(36,47)
(37,46)(38,45)(48,51)(49,53)(50,52)(54,56)(57,78)(58,80)(59,79)(60,75)(61,77)
(62,76)(63,83)(64,82)(65,81)(66,69)(67,71)(68,70)(72,74);
poly := sub<Sym(83)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*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