Overview
- Group
- SmallGroup(720,784)
- Rank
- 4
- Schläfli Type
- {10,4,6}
- Vertices, edges, …
- 10, 30, 18, 9
- Order of s0s1s2s3
- 20
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
5-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44);; s1 := ( 1, 2)( 3, 5)( 6,37)( 7,36)( 8,40)( 9,39)(10,38)(11,27)(12,26)(13,30)(14,29)(15,28)(16,32)(17,31)(18,35)(19,34)(20,33)(21,22)(23,25)(41,42)(43,45);; s2 := (16,41)(17,42)(18,43)(19,44)(20,45)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40);; s3 := ( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,16)( 7,17)( 8,18)( 9,19)(10,20)(11,26)(12,27)(13,28)(14,29)(15,30)(31,36)(32,37)(33,38)(34,39)(35,40);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*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(45)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44); s1 := Sym(45)!( 1, 2)( 3, 5)( 6,37)( 7,36)( 8,40)( 9,39)(10,38)(11,27)(12,26)(13,30)(14,29)(15,28)(16,32)(17,31)(18,35)(19,34)(20,33)(21,22)(23,25)(41,42)(43,45); s2 := Sym(45)!(16,41)(17,42)(18,43)(19,44)(20,45)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40); s3 := Sym(45)!( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,16)( 7,17)( 8,18)( 9,19)(10,20)(11,26)(12,27)(13,28)(14,29)(15,30)(31,36)(32,37)(33,38)(34,39)(35,40); poly := sub<Sym(45)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*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.