Overview
- Group
- SmallGroup(576,8653)
- Rank
- 3
- Schläfli Type
- {3,12}
- Vertices, edges, …
- 24, 144, 96
- 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
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*s2*s1)^2*s0*(s2*s1)^3*s2> of order 2
48 facets
- 48 of {3}*6
12 vertex figures
- 12 of {12}*24
P/N, where N=<s0*(s1*s0*s2)^5*s1*s2> of order 2
48 facets
- 48 of {3}*6
12 vertex figures
- 12 of {12}*24
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s2*s1)^5> of order 2
48 facets
- 48 of {3}*6
12 vertex figures
- 12 of {12}*24
P/N, where N=<(s0*s2*s1)^2*s0*(s2*s1)^5> of order 2
48 facets
- 48 of {3}*6
12 vertex figures
- 12 of {12}*24
P/N, where N=<s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2> of order 3
32 facets
- 32 of {3}*6
8 vertex figures
- 8 of {12}*24
P/N, where N=<s0*(s1*s2)^5*s1*s0*(s2*s1)^2, (s0*s2*s1)^2*s0*(s2*s1)^5> of order 4
24 facets
- 24 of {3}*6
6 vertex figures
- 6 of {12}*24
P/N, where N=<s0*(s1*s2)^5*s1*s0*s2, (s0*s2*s1)^2*s0*(s2*s1)^3*s2> of order 4
24 facets
- 24 of {3}*6
8 vertex figures
P/N, where N=<(s0*(s2*s1)^2)^2, s0*(s1*s2)^2*(s1*s0*s2)^2*s1> of order 4
24 facets
- 24 of {3}*6
8 vertex figures
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*(s2*s1)^3> of order 4
24 facets
- 24 of {3}*6
6 vertex figures
- 6 of {12}*24
P/N, where N=<(s0*s2*s1)^2*s0*(s2*s1)^3*s2, s0*(s2*s1)^3*(s0*s2*s1)^2*s2> of order 4
24 facets
- 24 of {3}*6
6 vertex figures
- 6 of {12}*24
P/N, where N=<s0*(s1*s2)^5*s1*s0*s2, s0*s1*s0*s2*s1*s0*(s2*s1)^4*s0*s2*s1*s2> of order 4
24 facets
- 24 of {3}*6
8 vertex figures
P/N, where N=<s0*s2*s1*s0*(s2*s1)^3*s0*s2*s1*s2, s0*(s1*s2)^4*(s1*s0*s2)^2*s1*s2> of order 6
16 facets
- 16 of {3}*6
6 vertex figures
P/N, where N=<s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2, s0*(s1*s0*s2)^2*s1*s0*(s2*s1)^4*s2> of order 6
16 facets
- 16 of {3}*6
4 vertex figures
- 4 of {12}*24
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*(s2*s1)^3, s0*s1*(s2*s1*s0)^4*s2> of order 8
12 facets
- 12 of {3}*6
3 vertex figures
- 3 of {12}*24
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2, s0*(s1*s2)^5*s1*s0*s2> of order 8
12 facets
- 12 of {3}*6
4 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^4, s0*s2*s1*s0*(s2*s1)^3*s0*s2*s1> of order 8
12 facets
- 12 of {3}*6
4 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15);; s1 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12);; s2 := ( 1,16)( 2,14)( 3,15)( 4,13)( 5,12)( 6,10)( 7,11)( 8, 9);; 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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(16)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15); s1 := Sym(16)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12); s2 := Sym(16)!( 1,16)( 2,14)( 3,15)( 4,13)( 5,12)( 6,10)( 7,11)( 8, 9); 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, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.