Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,2,12,3}

Atlas Canonical Name {3,2,2,12,3}*1152

Overview

Group
SmallGroup(1152,157603)
Rank
6
Schläfli Type
{3,2,2,12,3}
Vertices, edges, …
3, 3, 2, 16, 24, 4
Order of s0s1s2s3s4s5
24
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)( 9,10)(11,24)(12,27)(14,19)(15,18)(16,36)(17,39)(20,42)(21,43)(22,28)(23,25)(26,47)(29,46)(30,31)(32,48)(33,50)(34,37)(35,40)(38,52)(41,53)(44,45);;
s4 := ( 6,14)( 7, 9)( 8,30)(10,15)(11,53)(12,52)(13,18)(16,47)(17,46)(19,31)(20,51)(21,49)(22,41)(23,38)(24,37)(25,39)(26,35)(27,40)(28,36)(29,34)(32,45)(33,44)(42,48)(43,50);;
s5 := ( 6,51)( 7,45)( 8,44)( 9,41)(10,53)(11,16)(12,17)(13,49)(14,29)(15,47)(18,26)(19,46)(20,34)(21,35)(22,32)(23,33)(24,36)(25,50)(27,39)(28,48)(30,38)(31,52)(37,42)(40,43);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s5*s3*s4*s3*s4*s3*s4*s5*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(53)!(2,3);
s1 := Sym(53)!(1,2);
s2 := Sym(53)!(4,5);
s3 := Sym(53)!( 7, 8)( 9,10)(11,24)(12,27)(14,19)(15,18)(16,36)(17,39)(20,42)(21,43)(22,28)(23,25)(26,47)(29,46)(30,31)(32,48)(33,50)(34,37)(35,40)(38,52)(41,53)(44,45);
s4 := Sym(53)!( 6,14)( 7, 9)( 8,30)(10,15)(11,53)(12,52)(13,18)(16,47)(17,46)(19,31)(20,51)(21,49)(22,41)(23,38)(24,37)(25,39)(26,35)(27,40)(28,36)(29,34)(32,45)(33,44)(42,48)(43,50);
s5 := Sym(53)!( 6,51)( 7,45)( 8,44)( 9,41)(10,53)(11,16)(12,17)(13,49)(14,29)(15,47)(18,26)(19,46)(20,34)(21,35)(22,32)(23,33)(24,36)(25,50)(27,39)(28,48)(30,38)(31,52)(37,42)(40,43);
poly := sub<Sym(53)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s5*s3*s4*s3*s4*s3*s4*s5*s3*s4 >;