Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {3,12,3,2,2}*1920

Overview

Group
SmallGroup(1920,240973)
Rank
6
Schläfli Type
{3,12,3,2,2}
Vertices, edges, …
5, 40, 40, 5, 2, 2
Order of s0s1s2s3s4s5
10
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 := ( 1,11)( 2,24)( 3, 9)( 4,10)( 5,12)( 6,25)( 7,40)( 8,39)(13,19)(14,36)(15,27)(16,28)(17,18)(20,22)(26,35)(29,38)(30,37)(31,32)(33,34);;
s1 := ( 1, 2)( 3,15)( 4,16)( 5, 6)( 7, 9)( 8,10)(11,31)(12,34)(14,17)(18,20)(19,23)(21,35)(22,36)(24,32)(25,33)(27,40)(28,39)(29,38)(30,37);;
s2 := ( 2, 5)( 3, 9)( 4,10)( 7,14)( 8,13)(12,24)(15,26)(16,17)(18,28)(19,39)(21,23)(27,35)(29,33)(30,32)(31,37)(34,38)(36,40);;
s3 := ( 1,40)( 2,27)( 3,32)( 4,33)( 5,39)( 6,28)( 7,11)( 8,12)( 9,31)(10,34)(13,26)(15,24)(16,25)(19,35)(21,23)(29,38)(30,37);;
s4 := (41,42);;
s5 := (43,44);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(44)!( 1,11)( 2,24)( 3, 9)( 4,10)( 5,12)( 6,25)( 7,40)( 8,39)(13,19)(14,36)(15,27)(16,28)(17,18)(20,22)(26,35)(29,38)(30,37)(31,32)(33,34);
s1 := Sym(44)!( 1, 2)( 3,15)( 4,16)( 5, 6)( 7, 9)( 8,10)(11,31)(12,34)(14,17)(18,20)(19,23)(21,35)(22,36)(24,32)(25,33)(27,40)(28,39)(29,38)(30,37);
s2 := Sym(44)!( 2, 5)( 3, 9)( 4,10)( 7,14)( 8,13)(12,24)(15,26)(16,17)(18,28)(19,39)(21,23)(27,35)(29,33)(30,32)(31,37)(34,38)(36,40);
s3 := Sym(44)!( 1,40)( 2,27)( 3,32)( 4,33)( 5,39)( 6,28)( 7,11)( 8,12)( 9,31)(10,34)(13,26)(15,24)(16,25)(19,35)(21,23)(29,38)(30,37);
s4 := Sym(44)!(41,42);
s5 := Sym(44)!(43,44);
poly := sub<Sym(44)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2 >;