Polytope of Type {5,4} with group SmallGroup(1200,941)

Overview

Group: SmallGroup(1200,941)
Rank: 3
Schläfli Type: {5,4}
Vertices, edges, …: 150, 300, 120
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

5-fold

{5,4}*240

10-fold

{5,4}*120

60-fold

{5,2}*20

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

60 facets

60 of {5}*10

75 vertex figures

75 of {4}*8

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

60 facets

60 of {5}*10

80 vertex figures

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

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

40 facets

40 of {5}*10

50 vertex figures

50 of {4}*8

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

30 facets

30 of {5}*10

45 vertex figures

30 of {4}*8
15 of {2}*4

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

30 facets

30 of {5}*10

40 vertex figures

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

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

24 facets

24 of {5}*10

30 vertex figures

30 of {4}*8

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

20 facets

20 of {5}*10

30 vertex figures

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

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

12 facets

12 of {5}*10

20 vertex figures

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

P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2> of order 12

10 facets

10 of {5}*10

15 vertex figures

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

P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2, (s0*s1)^2*s0*s2*(s1*s0)^2*s2*s1*s2> of order 20

6 facets

6 of {5}*10

10 vertex figures

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

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 4, 5)( 7, 8)( 9,10);;
s1 := (1,2)(3,4)(6,7)(8,9);;
s2 := (2,3);;
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*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(10)!( 2, 3)( 4, 5)( 7, 8)( 9,10);
s1 := Sym(10)!(1,2)(3,4)(6,7)(8,9);
s2 := Sym(10)!(2,3);
poly := sub<Sym(10)|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*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.