Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,10,2}

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

Overview

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