Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,10,12}

Atlas Canonical Name {2,10,12}*1920d

Overview

Group
SmallGroup(1920,240976)
Rank
4
Schläfli Type
{2,10,12}
Vertices, edges, …
2, 40, 240, 48
Order of s0s1s2s3
8
Order of s0s1s2s3s2s1
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

8-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

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