Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,12}

Atlas Canonical Name {4,12}*1200

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1200,961)
Rank
3
Schläfli Type
{4,12}
Vertices, edges, …
50, 300, 150
Order of s0s1s2
30
Order of s0s1s2s1
10
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

3-fold

6-fold

50-fold

100-fold

150-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=<(s0*s1*s2*s1)^4*s0*(s2*s1)^2*s2> of order 2

75 facets

25 vertex figures

P/N, where N=<(s0*s1)^2> of order 2

78 facets

26 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2*(s0*(s2*s1)^2)^2*s0*s1*s2> of order 2

75 facets

25 vertex figures

P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2*(s0*(s2*s1)^2)^2*s0*s1*s2> of order 4

39 facets

13 vertex figures

P/N, where N=<s0*s1*s0*s2*s1*(s0*(s2*s1)^2)^2*s2> of order 5

30 facets

10 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2> of order 5

30 facets

10 vertex figures

P/N, where N=<(s0*s1)^2*s2*s1*s0*s2*s1*s2> of order 10

15 facets

5 vertex figures

P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2> of order 10

18 facets

6 vertex figures

P/N, where N=<(s0*s1)^2, s1*s2*s1*(s0*(s2*s1)^2)^2*s2> of order 10

18 facets

6 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 2,12)( 3,23)( 4, 9)( 5,20)( 6,21)( 8,18)(10,15)(11,16)(14,24)(17,22)(27,37)(28,48)(29,34)(30,45)(31,46)(33,43)(35,40)(36,41)(39,49)(42,47)(52,62)(53,73)(54,59)(55,70)(56,71)(58,68)(60,65)(61,66)(64,74)(67,72);;
s1 := ( 2, 9)( 3,12)( 4,20)( 5,23)( 6,13)( 7,16)( 8,24)(11,25)(15,17)(19,21)(26,51)(27,59)(28,62)(29,70)(30,73)(31,63)(32,66)(33,74)(34,52)(35,60)(36,75)(37,53)(38,56)(39,64)(40,67)(41,57)(42,65)(43,68)(44,71)(45,54)(46,69)(47,72)(48,55)(49,58)(50,61);;
s2 := ( 1,32)( 2,46)( 3,40)( 4,29)( 5,43)( 6,37)( 7,26)( 8,45)( 9,34)(10,48)(11,42)(12,31)(13,50)(14,39)(15,28)(16,47)(17,36)(18,30)(19,44)(20,33)(21,27)(22,41)(23,35)(24,49)(25,38)(51,57)(52,71)(53,65)(55,68)(56,62)(58,70)(60,73)(61,67)(63,75)(66,72);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(75)!( 2,12)( 3,23)( 4, 9)( 5,20)( 6,21)( 8,18)(10,15)(11,16)(14,24)(17,22)(27,37)(28,48)(29,34)(30,45)(31,46)(33,43)(35,40)(36,41)(39,49)(42,47)(52,62)(53,73)(54,59)(55,70)(56,71)(58,68)(60,65)(61,66)(64,74)(67,72);
s1 := Sym(75)!( 2, 9)( 3,12)( 4,20)( 5,23)( 6,13)( 7,16)( 8,24)(11,25)(15,17)(19,21)(26,51)(27,59)(28,62)(29,70)(30,73)(31,63)(32,66)(33,74)(34,52)(35,60)(36,75)(37,53)(38,56)(39,64)(40,67)(41,57)(42,65)(43,68)(44,71)(45,54)(46,69)(47,72)(48,55)(49,58)(50,61);
s2 := Sym(75)!( 1,32)( 2,46)( 3,40)( 4,29)( 5,43)( 6,37)( 7,26)( 8,45)( 9,34)(10,48)(11,42)(12,31)(13,50)(14,39)(15,28)(16,47)(17,36)(18,30)(19,44)(20,33)(21,27)(22,41)(23,35)(24,49)(25,38)(51,57)(52,71)(53,65)(55,68)(56,62)(58,70)(60,73)(61,67)(63,75)(66,72);
poly := sub<Sym(75)|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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0 >;

References

None.

to this polytope.

Twisty Puzzle