Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,155402)
Rank
5
Schläfli Type
{18,4,2,4}
Vertices, edges, …
18, 36, 4, 4, 4
Order of s0s1s2s3s4
36
Order of s0s1s2s3s4s3s2s1
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

4-fold

6-fold

12-fold

Covers minimal covers in bold

None in this atlas.

Representations

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