Part of the Atlas of Small Regular Polytopes

Polytope of Type {7,2,12,3}

Atlas Canonical Name {7,2,12,3}*1344

Overview

Group
SmallGroup(1344,11355)
Rank
5
Schläfli Type
{7,2,12,3}
Vertices, edges, …
7, 7, 16, 24, 4
Order of s0s1s2s3s4
56
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

4-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,10)(11,12)(13,26)(14,29)(16,21)(17,20)(18,38)(19,41)(22,44)(23,45)(24,30)(25,27)(28,49)(31,48)(32,33)(34,50)(35,52)(36,39)(37,42)(40,54)(43,55)(46,47);;
s3 := ( 8,16)( 9,11)(10,32)(12,17)(13,55)(14,54)(15,20)(18,49)(19,48)(21,33)(22,53)(23,51)(24,43)(25,40)(26,39)(27,41)(28,37)(29,42)(30,38)(31,36)(34,47)(35,46)(44,50)(45,52);;
s4 := ( 8,53)( 9,47)(10,46)(11,43)(12,55)(13,18)(14,19)(15,51)(16,31)(17,49)(20,28)(21,48)(22,36)(23,37)(24,34)(25,35)(26,38)(27,52)(29,41)(30,50)(32,40)(33,54)(39,44)(42,45);;
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, 
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(55)!(2,3)(4,5)(6,7);
s1 := Sym(55)!(1,2)(3,4)(5,6);
s2 := Sym(55)!( 9,10)(11,12)(13,26)(14,29)(16,21)(17,20)(18,38)(19,41)(22,44)(23,45)(24,30)(25,27)(28,49)(31,48)(32,33)(34,50)(35,52)(36,39)(37,42)(40,54)(43,55)(46,47);
s3 := Sym(55)!( 8,16)( 9,11)(10,32)(12,17)(13,55)(14,54)(15,20)(18,49)(19,48)(21,33)(22,53)(23,51)(24,43)(25,40)(26,39)(27,41)(28,37)(29,42)(30,38)(31,36)(34,47)(35,46)(44,50)(45,52);
s4 := Sym(55)!( 8,53)( 9,47)(10,46)(11,43)(12,55)(13,18)(14,19)(15,51)(16,31)(17,49)(20,28)(21,48)(22,36)(23,37)(24,34)(25,35)(26,38)(27,52)(29,41)(30,50)(32,40)(33,54)(39,44)(42,45);
poly := sub<Sym(55)|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, s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;