Polytope of Type {12,4} with group SmallGroup(1200,961)

Overview

Group: SmallGroup(1200,961)
Rank: 3
Schläfli Type: {12,4}
Vertices, edges, …: 150, 300, 50
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

{4,4}*400

6-fold

{4,4}*200

50-fold

{6,2}*24

100-fold

{3,2}*12

150-fold

{2,2}*8

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)^5> of order 2

25 facets

25 of {12}*24

75 vertex figures

75 of {4}*8

P/N, where N=<(s0*s1)^6> of order 2

26 facets

2 of {6}*12
24 of {12}*24

78 vertex figures

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

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

25 facets

25 of {12}*24

75 vertex figures

75 of {4}*8

P/N, where N=<(s0*s1)^6, s1*s2*(s1*s0)^2*(s2*s1*s0*s1)^3*s2> of order 4

13 facets

1 of {6}*12
12 of {12}*24

39 vertex figures

36 of {4}*8
3 of {2}*4

P/N, where N=<(s0*s1)^2*(s0*s2*s1)^3*s0*s1*s2> of order 5

10 facets

10 of {12}*24

30 vertex figures

30 of {4}*8

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

10 facets

10 of {12}*24

30 vertex figures

30 of {4}*8

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

5 facets

5 of {12}*24

15 vertex figures

15 of {4}*8

P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^6> of order 10

6 facets

2 of {6}*12
4 of {12}*24

18 vertex figures

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

P/N, where N=<(s0*s1)^6, s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2> of order 10

6 facets

2 of {6}*12
4 of {12}*24

18 vertex figures

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

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

References

None.

to this polytope.