Overview
- Group
- SmallGroup(1152,154366)
- Rank
- 5
- Schläfli Type
- {8,2,4,9}
- Vertices, edges, …
- 8, 8, 4, 18, 9
- Order of s0s1s2s3s4
- 72
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7);; s1 := (1,2)(3,4)(5,6)(7,8);; s2 := (10,15)(11,17)(12,19)(13,21)(16,26)(18,28)(22,32)(29,38)(31,40)(33,41)(35,42)(37,43);; s3 := ( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)(26,32)(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43);; s4 := ( 9,14)(10,12)(11,22)(13,18)(15,19)(16,31)(17,32)(20,27)(21,28)(23,24)(25,39)(26,40)(29,35)(30,36)(33,37)(34,44)(38,42)(41,43);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(44)!(2,3)(4,5)(6,7); s1 := Sym(44)!(1,2)(3,4)(5,6)(7,8); s2 := Sym(44)!(10,15)(11,17)(12,19)(13,21)(16,26)(18,28)(22,32)(29,38)(31,40)(33,41)(35,42)(37,43); s3 := Sym(44)!( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)(26,32)(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43); s4 := Sym(44)!( 9,14)(10,12)(11,22)(13,18)(15,19)(16,31)(17,32)(20,27)(21,28)(23,24)(25,39)(26,40)(29,35)(30,36)(33,37)(34,44)(38,42)(41,43); poly := sub<Sym(44)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;