Overview
- Group
- SmallGroup(1920,240973)
- Rank
- 5
- Schläfli Type
- {3,12,6,2}
- Vertices, edges, …
- 5, 40, 80, 10, 2
- Order of s0s1s2s3s4
- 10
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
Covers minimal covers in bold
None in this atlas.
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 := ( 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 := ( 1, 2)( 5, 6)( 7, 9)( 8,10)(11,14)(12,13)(15,27)(16,28)(17,30)(18,29)(19,22)(20,21)(23,40)(24,39)(25,41)(26,42)(31,38)(32,37)(33,35)(34,36);; s4 := (43,44);; 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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(44)!( 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(44)!( 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(44)!( 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(44)!( 1, 2)( 5, 6)( 7, 9)( 8,10)(11,14)(12,13)(15,27)(16,28)(17,30)(18,29)(19,22)(20,21)(23,40)(24,39)(25,41)(26,42)(31,38)(32,37)(33,35)(34,36); s4 := Sym(44)!(43,44); 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, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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 >;