Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,157864)
Rank
5
Schläfli Type
{4,3,12,2}
Vertices, edges, …
4, 12, 36, 24, 2
Order of s0s1s2s3s4
6
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

4-fold

6-fold

12-fold

Covers minimal covers in bold

None in this atlas.

Representations

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