Polytope of Type {4,2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,12,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,136342)
Rank : 5
Schlafli Type : {4,2,12,6}
Number of vertices, edges, etc : 4, 4, 12, 36, 6
Order of s₀s₁s₂s₃s₄ : 12
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 : {2,2,12,6}*576a, {4,2,6,6}*576a
   3-fold quotients : {4,2,12,2}*384, {4,2,4,6}*384a
   4-fold quotients : {2,2,6,6}*288a
   6-fold quotients : {2,2,12,2}*192, {2,2,4,6}*192a, {4,2,2,6}*192, {4,2,6,2}*192
   9-fold quotients : {4,2,4,2}*128
   12-fold quotients : {4,2,2,3}*96, {4,2,3,2}*96, {2,2,2,6}*96, {2,2,6,2}*96
   18-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   24-fold quotients : {2,2,2,3}*48, {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 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 5,41)( 6,42)( 7,43)( 8,47)( 9,48)(10,49)(11,44)(12,45)(13,46)(14,50)
(15,51)(16,52)(17,56)(18,57)(19,58)(20,53)(21,54)(22,55)(23,68)(24,69)(25,70)
(26,74)(27,75)(28,76)(29,71)(30,72)(31,73)(32,59)(33,60)(34,61)(35,65)(36,66)
(37,67)(38,62)(39,63)(40,64);;
s3 := ( 5,62)( 6,64)( 7,63)( 8,59)( 9,61)(10,60)(11,65)(12,67)(13,66)(14,71)
(15,73)(16,72)(17,68)(18,70)(19,69)(20,74)(21,76)(22,75)(23,44)(24,46)(25,45)
(26,41)(27,43)(28,42)(29,47)(30,49)(31,48)(32,53)(33,55)(34,54)(35,50)(36,52)
(37,51)(38,56)(39,58)(40,57);;
s4 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)
(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)
(68,69)(71,72)(74,75);;
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*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, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(76)!(2,3);
s1 := Sym(76)!(1,2)(3,4);
s2 := Sym(76)!( 5,41)( 6,42)( 7,43)( 8,47)( 9,48)(10,49)(11,44)(12,45)(13,46)
(14,50)(15,51)(16,52)(17,56)(18,57)(19,58)(20,53)(21,54)(22,55)(23,68)(24,69)
(25,70)(26,74)(27,75)(28,76)(29,71)(30,72)(31,73)(32,59)(33,60)(34,61)(35,65)
(36,66)(37,67)(38,62)(39,63)(40,64);
s3 := Sym(76)!( 5,62)( 6,64)( 7,63)( 8,59)( 9,61)(10,60)(11,65)(12,67)(13,66)
(14,71)(15,73)(16,72)(17,68)(18,70)(19,69)(20,74)(21,76)(22,75)(23,44)(24,46)
(25,45)(26,41)(27,43)(28,42)(29,47)(30,49)(31,48)(32,53)(33,55)(34,54)(35,50)
(36,52)(37,51)(38,56)(39,58)(40,57);
s4 := Sym(76)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)
(65,66)(68,69)(71,72)(74,75);
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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*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 >;

to this polytope