Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,6}

Atlas Canonical Name {12,6}*144c

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Overview

Group
SmallGroup(144,154)
Rank
3
Schläfli Type
{12,6}
Vertices, edges, …
12, 36, 6
Order of s0s1s2
12
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat
  • Self-Petrie

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

9-fold

12-fold

18-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(19,28)(20,30)(21,29)(22,31)(23,33)(24,32)(25,34)(26,36)(27,35)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(55,64)(56,66)(57,65)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71);;
s1 := ( 1,56)( 2,55)( 3,57)( 4,62)( 5,61)( 6,63)( 7,59)( 8,58)( 9,60)(10,65)(11,64)(12,66)(13,71)(14,70)(15,72)(16,68)(17,67)(18,69)(19,38)(20,37)(21,39)(22,44)(23,43)(24,45)(25,41)(26,40)(27,42)(28,47)(29,46)(30,48)(31,53)(32,52)(33,54)(34,50)(35,49)(36,51);;
s2 := ( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,58)(20,60)(21,59)(22,55)(23,57)(24,56)(25,61)(26,63)(27,62)(28,67)(29,69)(30,68)(31,64)(32,66)(33,65)(34,70)(35,72)(36,71);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(72)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(19,28)(20,30)(21,29)(22,31)(23,33)(24,32)(25,34)(26,36)(27,35)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(55,64)(56,66)(57,65)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71);
s1 := Sym(72)!( 1,56)( 2,55)( 3,57)( 4,62)( 5,61)( 6,63)( 7,59)( 8,58)( 9,60)(10,65)(11,64)(12,66)(13,71)(14,70)(15,72)(16,68)(17,67)(18,69)(19,38)(20,37)(21,39)(22,44)(23,43)(24,45)(25,41)(26,40)(27,42)(28,47)(29,46)(30,48)(31,53)(32,52)(33,54)(34,50)(35,49)(36,51);
s2 := Sym(72)!( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,58)(20,60)(21,59)(22,55)(23,57)(24,56)(25,61)(26,63)(27,62)(28,67)(29,69)(30,68)(31,64)(32,66)(33,65)(34,70)(35,72)(36,71);
poly := sub<Sym(72)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle