Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,2,8,3}

Atlas Canonical Name {2,2,2,8,3}*768

Overview

Group
SmallGroup(768,1090163)
Rank
6
Schläfli Type
{2,2,2,8,3}
Vertices, edges, …
2, 2, 2, 16, 24, 6
Order of s0s1s2s3s4s5
12
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

8-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7,17)( 8,13)( 9,12)(10,33)(11,35)(14,18)(15,22)(16,24)(19,21)(20,23)(25,50)(26,54)(27,49)(28,52)(29,53)(30,51)(31,34)(32,36)(37,45)(38,47)(39,43)(40,46)(41,48)(42,44);;
s4 := ( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)(22,44)(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)(42,54)(45,46);;
s5 := ( 7,11)( 8,20)( 9,16)(12,24)(13,23)(14,32)(15,19)(17,35)(18,36)(21,22)(25,27)(26,48)(28,30)(29,47)(37,39)(38,53)(40,42)(41,54)(43,45)(44,46)(49,50)(51,52);;
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s5*s4*s3*s5*s4*s3*s4*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(54)!(1,2);
s1 := Sym(54)!(3,4);
s2 := Sym(54)!(5,6);
s3 := Sym(54)!( 7,17)( 8,13)( 9,12)(10,33)(11,35)(14,18)(15,22)(16,24)(19,21)(20,23)(25,50)(26,54)(27,49)(28,52)(29,53)(30,51)(31,34)(32,36)(37,45)(38,47)(39,43)(40,46)(41,48)(42,44);
s4 := Sym(54)!( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)(22,44)(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)(42,54)(45,46);
s5 := Sym(54)!( 7,11)( 8,20)( 9,16)(12,24)(13,23)(14,32)(15,19)(17,35)(18,36)(21,22)(25,27)(26,48)(28,30)(29,47)(37,39)(38,53)(40,42)(41,54)(43,45)(44,46)(49,50)(51,52);
poly := sub<Sym(54)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s5*s4*s3*s5*s4*s3*s4*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;