Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1344,11327)
Rank
5
Schläfli Type
{7,2,12,4}
Vertices, edges, …
7, 7, 12, 24, 4
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 := ( 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);;
s3 := ( 8,15)( 9,11)(10,26)(12,16)(13,50)(14,18)(17,41)(19,27)(20,55)(21,49)(22,33)(23,32)(24,36)(25,30)(28,51)(29,40)(31,45)(34,54)(35,46)(37,44)(38,43)(39,48)(42,52)(47,53);;
s4 := ( 8,40)( 9,49)(10,52)(11,41)(12,25)(13,23)(14,54)(15,50)(16,33)(17,36)(18,51)(19,38)(20,31)(21,24)(22,39)(26,55)(27,46)(28,44)(29,32)(30,48)(34,37)(35,47)(42,45)(43,53);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)(13,23)(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);
s3 := Sym(55)!( 8,15)( 9,11)(10,26)(12,16)(13,50)(14,18)(17,41)(19,27)(20,55)(21,49)(22,33)(23,32)(24,36)(25,30)(28,51)(29,40)(31,45)(34,54)(35,46)(37,44)(38,43)(39,48)(42,52)(47,53);
s4 := Sym(55)!( 8,40)( 9,49)(10,52)(11,41)(12,25)(13,23)(14,54)(15,50)(16,33)(17,36)(18,51)(19,38)(20,31)(21,24)(22,39)(26,55)(27,46)(28,44)(29,32)(30,48)(34,37)(35,47)(42,45)(43,53);
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;