Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,2,18,4}

Atlas Canonical Name {3,2,2,18,4}*1728b

Overview

Group
SmallGroup(1728,46115)
Rank
6
Schläfli Type
{3,2,2,18,4}
Vertices, edges, …
3, 3, 2, 18, 36, 4
Order of s0s1s2s3s4s5
18
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)(10,14)(11,16)(12,15)(13,17)(18,34)(19,36)(20,35)(21,37)(22,30)(23,32)(24,31)(25,33)(26,38)(27,40)(28,39)(29,41)(43,44)(46,50)(47,52)(48,51)(49,53)(54,70)(55,72)(56,71)(57,73)(58,66)(59,68)(60,67)(61,69)(62,74)(63,76)(64,75)(65,77);;
s4 := ( 6,54)( 7,55)( 8,57)( 9,56)(10,62)(11,63)(12,65)(13,64)(14,58)(15,59)(16,61)(17,60)(18,42)(19,43)(20,45)(21,44)(22,50)(23,51)(24,53)(25,52)(26,46)(27,47)(28,49)(29,48)(30,70)(31,71)(32,73)(33,72)(34,66)(35,67)(36,69)(37,68)(38,74)(39,75)(40,77)(41,76);;
s5 := ( 6, 9)( 7, 8)(10,13)(11,12)(14,17)(15,16)(18,21)(19,20)(22,25)(23,24)(26,29)(27,28)(30,33)(31,32)(34,37)(35,36)(38,41)(39,40)(42,45)(43,44)(46,49)(47,48)(50,53)(51,52)(54,57)(55,56)(58,61)(59,60)(62,65)(63,64)(66,69)(67,68)(70,73)(71,72)(74,77)(75,76);;
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, 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, 
s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5, 
s5*s4*s3*s5*s4*s5*s4*s3*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*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(77)!(2,3);
s1 := Sym(77)!(1,2);
s2 := Sym(77)!(4,5);
s3 := Sym(77)!( 7, 8)(10,14)(11,16)(12,15)(13,17)(18,34)(19,36)(20,35)(21,37)(22,30)(23,32)(24,31)(25,33)(26,38)(27,40)(28,39)(29,41)(43,44)(46,50)(47,52)(48,51)(49,53)(54,70)(55,72)(56,71)(57,73)(58,66)(59,68)(60,67)(61,69)(62,74)(63,76)(64,75)(65,77);
s4 := Sym(77)!( 6,54)( 7,55)( 8,57)( 9,56)(10,62)(11,63)(12,65)(13,64)(14,58)(15,59)(16,61)(17,60)(18,42)(19,43)(20,45)(21,44)(22,50)(23,51)(24,53)(25,52)(26,46)(27,47)(28,49)(29,48)(30,70)(31,71)(32,73)(33,72)(34,66)(35,67)(36,69)(37,68)(38,74)(39,75)(40,77)(41,76);
s5 := Sym(77)!( 6, 9)( 7, 8)(10,13)(11,12)(14,17)(15,16)(18,21)(19,20)(22,25)(23,24)(26,29)(27,28)(30,33)(31,32)(34,37)(35,36)(38,41)(39,40)(42,45)(43,44)(46,49)(47,48)(50,53)(51,52)(54,57)(55,56)(58,61)(59,60)(62,65)(63,64)(66,69)(67,68)(70,73)(71,72)(74,77)(75,76);
poly := sub<Sym(77)|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, 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, s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5, 
s5*s4*s3*s5*s4*s5*s4*s3*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;