Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,157448)
Rank
6
Schläfli Type
{2,2,2,4,18}
Vertices, edges, …
2, 2, 2, 4, 36, 18
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 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78);;
s4 := ( 8, 9)(11,15)(12,17)(13,16)(14,18)(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(27,39)(28,41)(29,40)(30,42)(44,45)(47,51)(48,53)(49,52)(50,54)(55,71)(56,73)(57,72)(58,74)(59,67)(60,69)(61,68)(62,70)(63,75)(64,77)(65,76)(66,78);;
s5 := ( 7,55)( 8,56)( 9,58)(10,57)(11,63)(12,64)(13,66)(14,65)(15,59)(16,60)(17,62)(18,61)(19,43)(20,44)(21,46)(22,45)(23,51)(24,52)(25,54)(26,53)(27,47)(28,48)(29,50)(30,49)(31,71)(32,72)(33,74)(34,73)(35,67)(36,68)(37,70)(38,69)(39,75)(40,76)(41,78)(42,77);;
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(78)!(1,2);
s1 := Sym(78)!(3,4);
s2 := Sym(78)!(5,6);
s3 := Sym(78)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78);
s4 := Sym(78)!( 8, 9)(11,15)(12,17)(13,16)(14,18)(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(27,39)(28,41)(29,40)(30,42)(44,45)(47,51)(48,53)(49,52)(50,54)(55,71)(56,73)(57,72)(58,74)(59,67)(60,69)(61,68)(62,70)(63,75)(64,77)(65,76)(66,78);
s5 := Sym(78)!( 7,55)( 8,56)( 9,58)(10,57)(11,63)(12,64)(13,66)(14,65)(15,59)(16,60)(17,62)(18,61)(19,43)(20,44)(21,46)(22,45)(23,51)(24,52)(25,54)(26,53)(27,47)(28,48)(29,50)(30,49)(31,71)(32,72)(33,74)(34,73)(35,67)(36,68)(37,70)(38,69)(39,75)(40,76)(41,78)(42,77);
poly := sub<Sym(78)|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, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s3*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;