Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,24,4}

Atlas Canonical Name {2,24,4}*1152a

Overview

Group
SmallGroup(1152,97552)
Rank
4
Schläfli Type
{2,24,4}
Vertices, edges, …
2, 72, 144, 12
Order of s0s1s2s3
8
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

9-fold

18-fold

36-fold

72-fold

Covers minimal covers in bold

None in this atlas.

Representations

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