Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,3,6,2}

Atlas Canonical Name {2,4,3,6,2}*1152

Overview

Group
SmallGroup(1152,157863)
Rank
6
Schläfli Type
{2,4,3,6,2}
Vertices, edges, …
2, 8, 12, 18, 6, 2
Order of s0s1s2s3s4s5
6
Order of s0s1s2s3s4s5s4s3s2s1
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

12-fold

Covers minimal covers in bold

None in this atlas.

Representations

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