Overview
- Group
- SmallGroup(960,10869)
- Rank
- 4
- Schläfli Type
- {2,6,8}
- Vertices, edges, …
- 2, 30, 120, 40
- Order of s0s1s2s3
- 10
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,13)( 4,26)( 5,11)( 6,12)( 7,14)( 8,27)( 9,42)(10,41)(15,21)(16,38)(17,29)(18,30)(19,20)(22,24)(28,37)(31,40)(32,39)(33,34)(35,36);; s2 := ( 5,12)( 6,11)( 9,28)(10,19)(13,24)(14,25)(15,18)(16,17)(20,39)(21,40)(22,27)(23,26)(29,34)(30,33)(31,38)(32,37)(35,42)(36,41);; s3 := ( 3,20)( 4,37)( 5,31)( 6,32)( 7,21)( 8,38)( 9,18)(11,40)(12,39)(13,19)(14,15)(16,27)(22,24)(26,28)(30,42)(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*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*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(42)!(1,2); s1 := Sym(42)!( 3,13)( 4,26)( 5,11)( 6,12)( 7,14)( 8,27)( 9,42)(10,41)(15,21)(16,38)(17,29)(18,30)(19,20)(22,24)(28,37)(31,40)(32,39)(33,34)(35,36); s2 := Sym(42)!( 5,12)( 6,11)( 9,28)(10,19)(13,24)(14,25)(15,18)(16,17)(20,39)(21,40)(22,27)(23,26)(29,34)(30,33)(31,38)(32,37)(35,42)(36,41); s3 := Sym(42)!( 3,20)( 4,37)( 5,31)( 6,32)( 7,21)( 8,38)( 9,18)(11,40)(12,39)(13,19)(14,15)(16,27)(22,24)(26,28)(30,42)(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*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*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2*s3 >;