Overview
- Group
- SmallGroup(576,8653)
- Rank
- 3
- Schläfli Type
- {12,3}
- Vertices, edges, …
- 96, 144, 24
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Petrie
Quotients maximal quotients in bold
4-fold
12-fold
16-fold
24-fold
48-fold
Covers minimal covers in bold
2-fold
3-fold
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)^4*s2*(s1*s0)^2*s2> of order 2
12 facets
- 12 of {12}*24
48 vertex figures
- 48 of {3}*6
P/N, where N=<(s0*s1)^4*s0*s2*(s1*s0)^3*s1*s2> of order 2
12 facets
- 12 of {12}*24
48 vertex figures
- 48 of {3}*6
P/N, where N=<(s0*s1)^4*s2*(s1*s0)^2*s1*s2*s1*s0*s1> of order 2
12 facets
- 12 of {12}*24
48 vertex figures
- 48 of {3}*6
P/N, where N=<s0*s2*(s1*s0)^5*s1*s2*s1*s0*s1> of order 2
12 facets
- 12 of {12}*24
48 vertex figures
- 48 of {3}*6
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^3*s2> of order 3
8 facets
- 8 of {12}*24
32 vertex figures
- 32 of {3}*6
P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^4*s2> of order 4
6 facets
- 6 of {12}*24
24 vertex figures
- 24 of {3}*6
P/N, where N=<(s0*s1)^4*s2*(s1*s0)^2*s2*s1*s0*s1, s0*s2*(s1*s0)^5*s1*s2*s1*s0*s1> of order 4
6 facets
- 6 of {12}*24
24 vertex figures
- 24 of {3}*6
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 4
6 facets
- 6 of {12}*24
24 vertex figures
- 24 of {3}*6
P/N, where N=<(s0*s1)^4*s2*(s1*s0)^2*s2, s0*s2*(s1*s0)^5*s1*s2> of order 4
8 facets
24 vertex figures
- 24 of {3}*6
P/N, where N=<s0*s2*(s1*s0)^2*s2*s1*s0*s1, s1*s0*s1*s2*(s1*s0)^3*s1*s2> of order 4
8 facets
24 vertex figures
- 24 of {3}*6
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s1*s0)^3*s1*s2*s1*s0*s1*s2> of order 4
6 facets
- 6 of {12}*24
24 vertex figures
- 24 of {3}*6
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 4
6 facets
- 6 of {12}*24
24 vertex figures
- 24 of {3}*6
P/N, where N=<s0*s2*(s1*s0)^5*s1*s2, (s0*s1)^4*s2*(s1*s0)^2*s1*s2*s1*s0*s1> of order 4
8 facets
24 vertex figures
- 24 of {3}*6
P/N, where N=<(s0*s1)^4, (s0*s1)^2*s2*(s1*s0)^5*s1*s2> of order 6
6 facets
16 vertex figures
- 16 of {3}*6
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^3*s2, (s0*s1)^5*s2*(s1*s0)^2*s1*s2*s1> of order 6
4 facets
- 4 of {12}*24
16 vertex figures
- 16 of {3}*6
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s1*s0)^3*s1*s2*s1*s0*s1*s2, (s0*s1)^2*s0*s2*(s1*s0)^4*s2> of order 8
3 facets
- 3 of {12}*24
12 vertex figures
- 12 of {3}*6
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s2*(s1*s0)^3*s1*s2*s1, (s0*s1)^2*s2*(s1*s0)^4*s2> of order 8
4 facets
12 vertex figures
- 12 of {3}*6
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s2*s1, s0*s1*s2*(s1*s0)^4*s2*s1> of order 8
4 facets
12 vertex figures
- 12 of {3}*6
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2,11)( 3,10)( 4,12)( 5,13)( 6,15)( 7,14)( 8,16);; s1 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16);; s2 := ( 1, 4)( 5,16)( 6,14)( 7,15)( 8,13)( 9,12);; 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,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 1, 9)( 2,11)( 3,10)( 4,12)( 5,13)( 6,15)( 7,14)( 8,16); s1 := Sym(16)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16); s2 := Sym(16)!( 1, 4)( 5,16)( 6,14)( 7,15)( 8,13)( 9,12); poly := sub<Sym(16)|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, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*s1 >;
References
None.
to this polytope.