Part of the Atlas of Small Regular Polytopes

Polytope of Type {14,6,3}

Atlas Canonical Name {14,6,3}*1512

Overview

Group
SmallGroup(1512,486)
Rank
4
Schläfli Type
{14,6,3}
Vertices, edges, …
14, 126, 27, 9
Order of s0s1s2s3
42
Order of s0s1s2s3s2s1
2
Also known as
{{14,6|2},{6,3}6}. if this polytope has another name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

7-fold

9-fold

18-fold

21-fold

63-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s2)^2> of order 3

5 facets

14 vertex figures

  • 14 of 3-fold non-regular quotient of {6,3}*108

Representations

Permutation Representation (GAP) 
s0 := ( 4,19)( 5,20)( 6,21)( 7,16)( 8,17)( 9,18)(10,13)(11,14)(12,15)(25,40)(26,41)(27,42)(28,37)(29,38)(30,39)(31,34)(32,35)(33,36)(46,61)(47,62)(48,63)(49,58)(50,59)(51,60)(52,55)(53,56)(54,57);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 7,19)( 8,21)( 9,20)(10,16)(11,18)(12,17)(14,15)(22,25)(23,27)(24,26)(28,40)(29,42)(30,41)(31,37)(32,39)(33,38)(35,36)(43,46)(44,48)(45,47)(49,61)(50,63)(51,62)(52,58)(53,60)(54,59)(56,57);;
s2 := (22,45)(23,43)(24,44)(25,48)(26,46)(27,47)(28,51)(29,49)(30,50)(31,54)(32,52)(33,53)(34,57)(35,55)(36,56)(37,60)(38,58)(39,59)(40,63)(41,61)(42,62);;
s3 := ( 1,22)( 2,23)( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(63)!( 4,19)( 5,20)( 6,21)( 7,16)( 8,17)( 9,18)(10,13)(11,14)(12,15)(25,40)(26,41)(27,42)(28,37)(29,38)(30,39)(31,34)(32,35)(33,36)(46,61)(47,62)(48,63)(49,58)(50,59)(51,60)(52,55)(53,56)(54,57);
s1 := Sym(63)!( 1, 4)( 2, 6)( 3, 5)( 7,19)( 8,21)( 9,20)(10,16)(11,18)(12,17)(14,15)(22,25)(23,27)(24,26)(28,40)(29,42)(30,41)(31,37)(32,39)(33,38)(35,36)(43,46)(44,48)(45,47)(49,61)(50,63)(51,62)(52,58)(53,60)(54,59)(56,57);
s2 := Sym(63)!(22,45)(23,43)(24,44)(25,48)(26,46)(27,47)(28,51)(29,49)(30,50)(31,54)(32,52)(33,53)(34,57)(35,55)(36,56)(37,60)(38,58)(39,59)(40,63)(41,61)(42,62);
s3 := Sym(63)!( 1,22)( 2,23)( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42);
poly := sub<Sym(63)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.