Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,10}

Atlas Canonical Name {2,8,10}*1920d

Overview

Group
SmallGroup(1920,240976)
Rank
4
Schläfli Type
{2,8,10}
Vertices, edges, …
2, 48, 240, 60
Order of s0s1s2s3
12
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 := ( 3, 5)( 4,40)( 6,15)( 7,14)( 8,32)( 9,37)(10,50)(11,30)(12,29)(13,27)(16,17)(18,48)(19,33)(20,21)(22,38)(23,45)(24,34)(25,43)(26,44)(28,31)(35,47)(36,46)(39,49)(41,42);;
s2 := ( 4, 6)( 5,44)( 8,18)( 9,17)(10,30)(11,26)(12,21)(13,24)(14,36)(16,42)(20,31)(23,37)(25,33)(27,43)(28,35)(29,41)(32,38)(40,46)(45,47)(48,49);;
s3 := ( 4,29)( 6,14)( 7,15)( 8,16)( 9,11)(12,40)(13,35)(17,32)(18,28)(20,26)(21,44)(22,39)(23,46)(25,42)(27,47)(30,37)(31,48)(36,45)(38,49)(41,43);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, 
s1*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 3, 5)( 4,40)( 6,15)( 7,14)( 8,32)( 9,37)(10,50)(11,30)(12,29)(13,27)(16,17)(18,48)(19,33)(20,21)(22,38)(23,45)(24,34)(25,43)(26,44)(28,31)(35,47)(36,46)(39,49)(41,42);
s2 := Sym(50)!( 4, 6)( 5,44)( 8,18)( 9,17)(10,30)(11,26)(12,21)(13,24)(14,36)(16,42)(20,31)(23,37)(25,33)(27,43)(28,35)(29,41)(32,38)(40,46)(45,47)(48,49);
s3 := Sym(50)!( 4,29)( 6,14)( 7,15)( 8,16)( 9,11)(12,40)(13,35)(17,32)(18,28)(20,26)(21,44)(22,39)(23,46)(25,42)(27,47)(30,37)(31,48)(36,45)(38,49)(41,43);
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, 
s1*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2 >;