Part of the Atlas of Small Regular Polytopes

Polytope of Type {7,2,4,12}

Atlas Canonical Name {7,2,4,12}*1344b

Overview

Group
SmallGroup(1344,11327)
Rank
5
Schläfli Type
{7,2,4,12}
Vertices, edges, …
7, 7, 4, 24, 12
Order of s0s1s2s3s4
84
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-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 := ( 8,13)( 9,17)(10,20)(11,21)(12,22)(14,28)(15,29)(16,30)(18,34)(19,35)(23,40)(24,41)(25,39)(26,42)(27,43)(31,52)(32,50)(33,48)(36,49)(37,51)(38,47)(44,54)(45,55)(46,53);;
s3 := ( 9,10)(11,12)(13,23)(15,19)(16,18)(17,31)(20,36)(21,39)(22,24)(25,41)(26,27)(28,44)(29,47)(30,37)(32,35)(33,51)(34,48)(38,50)(42,53)(43,45)(46,55)(49,52);;
s4 := ( 8,16)( 9,12)(10,27)(11,15)(13,30)(14,19)(17,22)(18,26)(20,43)(21,29)(23,33)(24,50)(25,36)(28,35)(31,46)(32,41)(34,42)(37,55)(38,44)(39,49)(40,48)(45,51)(47,54)(52,53);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)!( 8,13)( 9,17)(10,20)(11,21)(12,22)(14,28)(15,29)(16,30)(18,34)(19,35)(23,40)(24,41)(25,39)(26,42)(27,43)(31,52)(32,50)(33,48)(36,49)(37,51)(38,47)(44,54)(45,55)(46,53);
s3 := Sym(55)!( 9,10)(11,12)(13,23)(15,19)(16,18)(17,31)(20,36)(21,39)(22,24)(25,41)(26,27)(28,44)(29,47)(30,37)(32,35)(33,51)(34,48)(38,50)(42,53)(43,45)(46,55)(49,52);
s4 := Sym(55)!( 8,16)( 9,12)(10,27)(11,15)(13,30)(14,19)(17,22)(18,26)(20,43)(21,29)(23,33)(24,50)(25,36)(28,35)(31,46)(32,41)(34,42)(37,55)(38,44)(39,49)(40,48)(45,51)(47,54)(52,53);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;