Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,155402)
Rank
5
Schläfli Type
{4,2,18,4}
Vertices, edges, …
4, 4, 18, 36, 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);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 9,13)(10,15)(11,14)(12,16)(17,33)(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40)(42,43)(45,49)(46,51)(47,50)(48,52)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)(59,66)(60,68)(61,73)(62,75)(63,74)(64,76);;
s3 := ( 5,53)( 6,54)( 7,56)( 8,55)( 9,61)(10,62)(11,64)(12,63)(13,57)(14,58)(15,60)(16,59)(17,41)(18,42)(19,44)(20,43)(21,49)(22,50)(23,52)(24,51)(25,45)(26,46)(27,48)(28,47)(29,69)(30,70)(31,72)(32,71)(33,65)(34,66)(35,68)(36,67)(37,73)(38,74)(39,76)(40,75);;
s4 := ( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(76)!(2,3);
s1 := Sym(76)!(1,2)(3,4);
s2 := Sym(76)!( 6, 7)( 9,13)(10,15)(11,14)(12,16)(17,33)(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40)(42,43)(45,49)(46,51)(47,50)(48,52)(53,69)(54,71)(55,70)(56,72)(57,65)(58,67)(59,66)(60,68)(61,73)(62,75)(63,74)(64,76);
s3 := Sym(76)!( 5,53)( 6,54)( 7,56)( 8,55)( 9,61)(10,62)(11,64)(12,63)(13,57)(14,58)(15,60)(16,59)(17,41)(18,42)(19,44)(20,43)(21,49)(22,50)(23,52)(24,51)(25,45)(26,46)(27,48)(28,47)(29,69)(30,70)(31,72)(32,71)(33,65)(34,66)(35,68)(36,67)(37,73)(38,74)(39,76)(40,75);
s4 := Sym(76)!( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75);
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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;