Overview
- Group
- SmallGroup(960,10869)
- Rank
- 4
- Schläfli Type
- {6,12,3}
- Vertices, edges, …
- 10, 80, 40, 5
- Order of s0s1s2s3
- 10
- Order of s0s1s2s3s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 5, 6)( 7,20)( 8,19)( 9,21)(10,22)(11,13)(12,14)(15,37)(16,38)(17,35)(18,36)(23,24)(27,32)(28,31)(29,34)(30,33)(39,40);; s1 := ( 1, 2)( 5, 6)( 7,10)( 8, 9)(11,22)(12,21)(13,20)(14,19)(17,18)(23,33)(24,34)(25,32)(26,31)(29,30)(35,40)(36,39)(37,41)(38,42);; s2 := ( 3,25)( 4,26)( 5,23)( 6,24)( 7,38)( 8,37)( 9,35)(10,36)(11,13)(12,14)(15,19)(16,20)(17,21)(18,22)(27,30)(28,29)(31,34)(32,33)(41,42);; s3 := ( 3, 4)( 7,10)( 8, 9)(11,13)(12,14)(15,28)(16,27)(17,29)(18,30)(19,21)(20,22)(23,39)(24,40)(25,42)(26,41)(31,37)(32,38)(33,36)(34,35);; 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, s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(42)!( 5, 6)( 7,20)( 8,19)( 9,21)(10,22)(11,13)(12,14)(15,37)(16,38)(17,35)(18,36)(23,24)(27,32)(28,31)(29,34)(30,33)(39,40); s1 := Sym(42)!( 1, 2)( 5, 6)( 7,10)( 8, 9)(11,22)(12,21)(13,20)(14,19)(17,18)(23,33)(24,34)(25,32)(26,31)(29,30)(35,40)(36,39)(37,41)(38,42); s2 := Sym(42)!( 3,25)( 4,26)( 5,23)( 6,24)( 7,38)( 8,37)( 9,35)(10,36)(11,13)(12,14)(15,19)(16,20)(17,21)(18,22)(27,30)(28,29)(31,34)(32,33)(41,42); s3 := Sym(42)!( 3, 4)( 7,10)( 8, 9)(11,13)(12,14)(15,28)(16,27)(17,29)(18,30)(19,21)(20,22)(23,39)(24,40)(25,42)(26,41)(31,37)(32,38)(33,36)(34,35); poly := sub<Sym(42)|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, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2 >;
References
None.
to this polytope.