Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,3,2,4,12}

Atlas Canonical Name {2,3,2,4,12}*1152c

Overview

Group
SmallGroup(1152,157549)
Rank
6
Schläfli Type
{2,3,2,4,12}
Vertices, edges, …
2, 3, 3, 4, 24, 12
Order of s0s1s2s3s4s5
12
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

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