Part of the Atlas of Small Regular Polytopes

Polytope of Type {7,2,6,10}

Atlas Canonical Name {7,2,6,10}*1680

Overview

Group
SmallGroup(1680,966)
Rank
5
Schläfli Type
{7,2,6,10}
Vertices, edges, …
7, 7, 6, 30, 10
Order of s0s1s2s3s4
210
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

6-fold

10-fold

15-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 := (10,11)(14,15)(18,20)(19,21)(24,26)(25,27)(30,32)(31,33)(34,36)(35,37);;
s3 := ( 8,10)( 9,14)(12,19)(13,18)(16,25)(17,24)(20,21)(22,31)(23,30)(26,27)(28,35)(29,34)(32,33)(36,37);;
s4 := ( 8,16)( 9,12)(10,24)(11,26)(13,28)(14,18)(15,20)(17,22)(19,34)(21,36)(23,29)(25,30)(27,32)(31,35)(33,37);;
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*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(37)!(2,3)(4,5)(6,7);
s1 := Sym(37)!(1,2)(3,4)(5,6);
s2 := Sym(37)!(10,11)(14,15)(18,20)(19,21)(24,26)(25,27)(30,32)(31,33)(34,36)(35,37);
s3 := Sym(37)!( 8,10)( 9,14)(12,19)(13,18)(16,25)(17,24)(20,21)(22,31)(23,30)(26,27)(28,35)(29,34)(32,33)(36,37);
s4 := Sym(37)!( 8,16)( 9,12)(10,24)(11,26)(13,28)(14,18)(15,20)(17,22)(19,34)(21,36)(23,29)(25,30)(27,32)(31,35)(33,37);
poly := sub<Sym(37)|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*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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 >;