Polytope of Type {4,6} with group SmallGroup(384,17948)

Overview

Group: SmallGroup(384,17948)
Rank: 3
Schläfli Type: {4,6}
Vertices, edges, …: 32, 96, 48
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Related Polytopes

Constructions

Facet of

Vertex figure of

{2,4,6} ·768

Quotients maximal quotients in bold

2-fold

{4,6}*192a

4-fold

{4,6}*96

8-fold

16-fold

32-fold

{2,3}*12

48-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

5-fold

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*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 2

24 facets

24 of {4}*8

16 vertex figures

16 of {6}*12

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

28 facets

20 of {4}*8
8 of {2}*4

16 vertex figures

16 of {6}*12

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

24 facets

24 of {4}*8

16 vertex figures

16 of {6}*12

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

24 facets

24 of {4}*8

20 vertex figures

8 of {3}*6
12 of {6}*12

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

24 facets

24 of {4}*8

16 vertex figures

16 of {6}*12

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

24 facets

24 of {4}*8

16 vertex figures

16 of {6}*12

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

24 facets

24 of {4}*8

16 vertex figures

16 of {6}*12

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

24 facets

24 of {4}*8

16 vertex figures

16 of {6}*12

P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4

14 facets

10 of {4}*8
4 of {2}*4

8 vertex figures

8 of {6}*12

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

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

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

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

P/N, where N=<(s1*s2)^3, (s0*s2*s1)^3> of order 4

12 facets

12 of {4}*8

10 vertex figures

4 of {3}*6
6 of {6}*12

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

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

P/N, where N=<(s0*s2*s1)^3, s0*s1*s2*s1*s0*(s2*s1)^2*s0*s1> of order 4

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

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

14 facets

10 of {4}*8
4 of {2}*4

8 vertex figures

8 of {6}*12

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

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

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

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

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

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

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

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4

18 facets

6 of {4}*8
12 of {2}*4

8 vertex figures

8 of {6}*12

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

16 facets

8 of {2}*4
8 of {4}*8

8 vertex figures

8 of {6}*12

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

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

P/N, where N=<(s1*s2)^3, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0> of order 4

12 facets

12 of {4}*8

12 vertex figures

8 of {3}*6
4 of {6}*12

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

14 facets

10 of {4}*8
4 of {2}*4

8 vertex figures

8 of {6}*12

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

14 facets

10 of {4}*8
4 of {2}*4

8 vertex figures

8 of {6}*12

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

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

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

16 facets

8 of {2}*4
8 of {4}*8

8 vertex figures

8 of {6}*12

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

14 facets

10 of {4}*8
4 of {2}*4

8 vertex figures

8 of {6}*12

P/N, where N=<(s0*s1)^2, (s1*s2)^3> of order 8

8 facets

4 of {2}*4
4 of {4}*8

6 vertex figures

4 of {3}*6
2 of {6}*12

P/N, where N=<(s0*s1)^2*s2*s1*s0*s2*s1*s2, s0*s1*(s2*s1*s0)^2*s2*s1> of order 8

6 facets

6 of {4}*8

4 vertex figures

4 of {6}*12

P/N, where N=<(s0*s1)^2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8

8 facets

4 of {2}*4
4 of {4}*8

4 vertex figures

4 of {6}*12

P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 8

8 facets

4 of {4}*8
4 of {2}*4

4 vertex figures

4 of {6}*12

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 8

6 facets

6 of {4}*8

4 vertex figures

4 of {6}*12

P/N, where N=<(s1*s2)^3, s0*s1*(s2*s1*s0)^2*s2*s1> of order 8

6 facets

6 of {4}*8

6 vertex figures

4 of {3}*6
2 of {6}*12

P/N, where N=<(s0*s1)^2, s0*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 8

8 facets

4 of {2}*4
4 of {4}*8

4 vertex figures

4 of {6}*12

P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2> of order 8

10 facets

8 of {2}*4
2 of {4}*8

4 vertex figures

4 of {6}*12

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 8

6 facets

6 of {4}*8

4 vertex figures

4 of {6}*12

P/N, where N=<(s1*s2)^3, (s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 8

6 facets

6 of {4}*8

6 vertex figures

4 of {3}*6
2 of {6}*12

P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s1*s2, (s2*s1*s0)^2*(s1*s2)^2> of order 8

7 facets

5 of {4}*8
2 of {2}*4

4 vertex figures

4 of {6}*12

P/N, where N=<(s0*s2*s1)^3, (s0*s1)^2*s2*s1*s0*s2*s1*s2> of order 8

6 facets

6 of {4}*8

4 vertex figures

4 of {6}*12

Representations

Permutation Representation (GAP)

s0 := ( 1,57)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,73)(18,74)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,89)(34,90)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88);;
s1 := ( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,33)(18,34)(19,36)(20,35)(21,44)(22,43)(23,41)(24,42)(25,39)(26,40)(27,38)(28,37)(29,46)(30,45)(31,47)(32,48)(51,52)(53,60)(54,59)(55,57)(56,58)(61,62)(65,81)(66,82)(67,84)(68,83)(69,92)(70,91)(71,89)(72,90)(73,87)(74,88)(75,86)(76,85)(77,94)(78,93)(79,95)(80,96);;
s2 := ( 1,33)( 2,35)( 3,34)( 4,36)( 5,45)( 6,47)( 7,46)( 8,48)( 9,41)(10,43)(11,42)(12,44)(13,37)(14,39)(15,38)(16,40)(18,19)(21,29)(22,31)(23,30)(24,32)(26,27)(49,81)(50,83)(51,82)(52,84)(53,93)(54,95)(55,94)(56,96)(57,89)(58,91)(59,90)(60,92)(61,85)(62,87)(63,86)(64,88)(66,67)(69,77)(70,79)(71,78)(72,80)(74,75);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(96)!( 1,57)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,73)(18,74)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,89)(34,90)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88);
s1 := Sym(96)!( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,33)(18,34)(19,36)(20,35)(21,44)(22,43)(23,41)(24,42)(25,39)(26,40)(27,38)(28,37)(29,46)(30,45)(31,47)(32,48)(51,52)(53,60)(54,59)(55,57)(56,58)(61,62)(65,81)(66,82)(67,84)(68,83)(69,92)(70,91)(71,89)(72,90)(73,87)(74,88)(75,86)(76,85)(77,94)(78,93)(79,95)(80,96);
s2 := Sym(96)!( 1,33)( 2,35)( 3,34)( 4,36)( 5,45)( 6,47)( 7,46)( 8,48)( 9,41)(10,43)(11,42)(12,44)(13,37)(14,39)(15,38)(16,40)(18,19)(21,29)(22,31)(23,30)(24,32)(26,27)(49,81)(50,83)(51,82)(52,84)(53,93)(54,95)(55,94)(56,96)(57,89)(58,91)(59,90)(60,92)(61,85)(62,87)(63,86)(64,88)(66,67)(69,77)(70,79)(71,78)(72,80)(74,75);
poly := sub<Sym(96)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.

Overview

Special Properties

Related Polytopes

Quotients maximal quotients in bold

Covers minimal covers in bold

Irregular Quotients of which this is a minimal cover

Representations

References

Twisty Puzzle