Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,18,4,4}*1152

Overview

Group
SmallGroup(1152,134249)
Rank
5
Schläfli Type
{2,18,4,4}
Vertices, edges, …
2, 18, 36, 8, 4
Order of s0s1s2s3s4
36
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

9-fold

12-fold

18-fold

24-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

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