Part of the Atlas of Small Regular Polytopes

Polytope of Type {7,2,8,3}

Atlas Canonical Name {7,2,8,3}*1344

Overview

Group
SmallGroup(1344,11355)
Rank
5
Schläfli Type
{7,2,8,3}
Vertices, edges, …
7, 7, 16, 24, 6
Order of s0s1s2s3s4
84
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

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