Overview
- Group
- SmallGroup(784,165)
- Rank
- 4
- Schläfli Type
- {2,4,14}
- Vertices, edges, …
- 2, 14, 98, 49
- Order of s0s1s2s3
- 4
- 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
No regular quotients.
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (10,45)(11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,38)(18,39)(19,40)(20,41)(21,42)(22,43)(23,44)(24,31)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37);; s2 := ( 4,10)( 5,17)( 6,24)( 7,31)( 8,38)( 9,45)(12,18)(13,25)(14,32)(15,39)(16,46)(20,26)(21,33)(22,40)(23,47)(28,34)(29,41)(30,48)(36,42)(37,49)(44,50);; s3 := ( 3, 4)( 5, 9)( 6, 8)(10,46)(11,45)(12,51)(13,50)(14,49)(15,48)(16,47)(17,39)(18,38)(19,44)(20,43)(21,42)(22,41)(23,40)(24,32)(25,31)(26,37)(27,36)(28,35)(29,34)(30,33);; 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, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(51)!(1,2); s1 := Sym(51)!(10,45)(11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,38)(18,39)(19,40)(20,41)(21,42)(22,43)(23,44)(24,31)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37); s2 := Sym(51)!( 4,10)( 5,17)( 6,24)( 7,31)( 8,38)( 9,45)(12,18)(13,25)(14,32)(15,39)(16,46)(20,26)(21,33)(22,40)(23,47)(28,34)(29,41)(30,48)(36,42)(37,49)(44,50); s3 := Sym(51)!( 3, 4)( 5, 9)( 6, 8)(10,46)(11,45)(12,51)(13,50)(14,49)(15,48)(16,47)(17,39)(18,38)(19,44)(20,43)(21,42)(22,41)(23,40)(24,32)(25,31)(26,37)(27,36)(28,35)(29,34)(30,33); poly := sub<Sym(51)|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, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2 >;