Overview
- Group
- SmallGroup(1920,240973)
- Rank
- 4
- Schläfli Type
- {2,8,10}
- Vertices, edges, …
- 2, 48, 240, 60
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 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
120-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 := ( 5,13)( 6,14)( 7,16)( 8,15)( 9,42)(10,41)(11,43)(12,44)(17,36)(18,35)(19,34)(20,33)(21,27)(22,28)(23,25)(24,26)(29,30)(31,32);; s3 := ( 3, 4)( 5,27)( 6,28)( 7,26)( 8,25)( 9,18)(10,17)(11,19)(12,20)(21,39)(22,40)(23,37)(24,38)(29,35)(30,36)(31,33)(32,34)(41,42)(43,44);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)!( 5,13)( 6,14)( 7,16)( 8,15)( 9,42)(10,41)(11,43)(12,44)(17,36)(18,35)(19,34)(20,33)(21,27)(22,28)(23,25)(24,26)(29,30)(31,32); s3 := Sym(44)!( 3, 4)( 5,27)( 6,28)( 7,26)( 8,25)( 9,18)(10,17)(11,19)(12,20)(21,39)(22,40)(23,37)(24,38)(29,35)(30,36)(31,33)(32,34)(41,42)(43,44); poly := sub<Sym(44)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;