Polytope of Type {2,36,6}

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

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

Permutation Representation (Magma) :

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

to this polytope