Overview
- Group
- SmallGroup(1920,240973)
- Rank
- 5
- Schläfli Type
- {2,3,12,6}
- Vertices, edges, …
- 2, 5, 40, 80, 10
- 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 := (1,2);; s1 := ( 7, 8)( 9,22)(10,21)(11,23)(12,24)(13,15)(14,16)(17,39)(18,40)(19,37)(20,38)(25,26)(29,34)(30,33)(31,36)(32,35)(41,42);; s2 := ( 7, 8)( 9,12)(10,11)(13,24)(14,23)(15,22)(16,21)(19,20)(25,35)(26,36)(27,34)(28,33)(31,32)(37,42)(38,41)(39,43)(40,44);; s3 := ( 5,27)( 6,28)( 7,25)( 8,26)( 9,40)(10,39)(11,37)(12,38)(13,15)(14,16)(17,21)(18,22)(19,23)(20,24)(29,32)(30,31)(33,36)(34,35)(43,44);; s4 := ( 3, 4)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,29)(18,30)(19,32)(20,31)(21,24)(22,23)(25,42)(26,41)(27,43)(28,44)(33,40)(34,39)(35,37)(36,38);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(44)!(1,2); s1 := Sym(44)!( 7, 8)( 9,22)(10,21)(11,23)(12,24)(13,15)(14,16)(17,39)(18,40)(19,37)(20,38)(25,26)(29,34)(30,33)(31,36)(32,35)(41,42); s2 := Sym(44)!( 7, 8)( 9,12)(10,11)(13,24)(14,23)(15,22)(16,21)(19,20)(25,35)(26,36)(27,34)(28,33)(31,32)(37,42)(38,41)(39,43)(40,44); s3 := Sym(44)!( 5,27)( 6,28)( 7,25)( 8,26)( 9,40)(10,39)(11,37)(12,38)(13,15)(14,16)(17,21)(18,22)(19,23)(20,24)(29,32)(30,31)(33,36)(34,35)(43,44); s4 := Sym(44)!( 3, 4)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,29)(18,30)(19,32)(20,31)(21,24)(22,23)(25,42)(26,41)(27,43)(28,44)(33,40)(34,39)(35,37)(36,38); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s4*s2*s3 >;