Overview
- Group
- SmallGroup(1440,5849)
- Rank
- 3
- Schläfli Type
- {6,12}
- Vertices, edges, …
- 60, 360, 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
2-fold
3-fold
6-fold
12-fold
60-fold
120-fold
180-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)^3*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 2
60 facets
- 60 of {6}*12
30 vertex figures
- 30 of {12}*24
P/N, where N=<(s1*s2*(s1*s0)^2)^2*s1*s2> of order 2
60 facets
- 60 of {6}*12
30 vertex figures
- 30 of {12}*24
P/N, where N=<s0*(s2*s1)^2*(s0*s1)^2*s2*s1> of order 2
60 facets
- 60 of {6}*12
30 vertex figures
- 30 of {12}*24
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 4
30 facets
- 30 of {6}*12
18 vertex figures
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s2*(s1*s0)^2*(s1*s2)^2> of order 4
30 facets
- 30 of {6}*12
16 vertex figures
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, (s0*s1)^2*(s2*s1)^2*(s0*s1)^2*s2*s1> of order 4
30 facets
- 30 of {6}*12
16 vertex figures
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 6
24 facets
10 vertex figures
- 10 of {12}*24
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 6
24 facets
12 vertex figures
P/N, where N=<(s0*s1)^2, (s1*s2*(s1*s0)^2)^2*s1*s2> of order 6
24 facets
10 vertex figures
- 10 of {12}*24
P/N, where N=<(s0*s1)^2, s0*s1*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 6
24 facets
10 vertex figures
- 10 of {12}*24
Representations
Permutation Representation (GAP)
s0 := ( 9,11);; s1 := ( 2, 6)( 4, 5)( 7, 8)(10,11);; s2 := ( 1, 2)( 3, 5)( 4, 6)( 8,10);; 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*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(11)!( 9,11); s1 := Sym(11)!( 2, 6)( 4, 5)( 7, 8)(10,11); s2 := Sym(11)!( 1, 2)( 3, 5)( 4, 6)( 8,10); poly := sub<Sym(11)|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*s0*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1 >;
References
None.
to this polytope.