Overview
- Group
- SmallGroup(288,889)
- Rank
- 3
- Schläfli Type
- {4,4}
- Vertices, edges, …
- 36, 72, 36
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 6
- Also known as
- {4,4}(6,0), {4,4|6}. if this polytope has another name.
Special Properties
- Toroidal
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
4-fold
9-fold
18-fold
36-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
- {4,8}*1152a
- {8,4}*1152a
- {8,8}*1152a
- {8,8}*1152b
- {8,8}*1152c
- {8,8}*1152d
- {4,16}*1152a
- {16,4}*1152a
- {4,16}*1152b
- {16,4}*1152b
- {4,8}*1152b
- {8,4}*1152b
- {4,4}*1152
5-fold
6-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)^2*(s2*s1*s0*s1)^2*s2> of order 2
18 facets
- 18 of {4}*8
18 vertex figures
- 18 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^3, s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1> of order 4
9 facets
- 9 of {4}*8
9 vertex figures
- 9 of {4}*8
P/N, where N=<(s0*s1)^2, s0*s1*(s2*s1*s0)^4*s2*s1*s2> of order 4
10 facets
9 vertex figures
- 9 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2, s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1> of order 4
9 facets
- 9 of {4}*8
10 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2*s1*s0*s2*s1*s2> of order 6
6 facets
- 6 of {4}*8
6 vertex figures
- 6 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*(s2*s1*s0*s1)^2*s2> of order 6
6 facets
- 6 of {4}*8
6 vertex figures
- 6 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^3> of order 6
6 facets
- 6 of {4}*8
6 vertex figures
- 6 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 6
6 facets
- 6 of {4}*8
8 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 8, 9)(11,12);; s1 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);; s2 := ( 1, 2)( 4, 5)( 7,10)( 8,11)( 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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!( 8, 9)(11,12); s1 := Sym(12)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12); s2 := Sym(12)!( 1, 2)( 4, 5)( 7,10)( 8,11)( 9,12); poly := sub<Sym(12)|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, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.