Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*1296
if this polytope has a name.
Group : SmallGroup(1296,2977)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 27, 162, 27
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   3-fold quotients : {2,4,12}*432, {2,12,4}*432
   9-fold quotients : {2,4,4}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope