Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,12,2}

Atlas Canonical Name {2,6,12,2}*1152a

Overview

Group
SmallGroup(1152,157863)
Rank
5
Schläfli Type
{2,6,12,2}
Vertices, edges, …
2, 12, 72, 24, 2
Order of s0s1s2s3s4
6
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

12-fold

24-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

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