Overview
- Group
- SmallGroup(1512,560)
- Rank
- 4
- Schläfli Type
- {9,2,42}
- Vertices, edges, …
- 9, 9, 42, 42
- Order of s0s1s2s3
- 126
- 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
3-fold
6-fold
7-fold
9-fold
14-fold
18-fold
21-fold
42-fold
63-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7)(8,9);; s1 := (1,2)(3,4)(5,6)(7,8);; s2 := (12,13)(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)(30,31)(32,35)(33,34)(36,37)(38,41)(39,40)(42,43)(44,47)(45,46)(48,51)(49,50);; s3 := (10,26)(11,20)(12,18)(13,28)(14,16)(15,38)(17,22)(19,32)(21,30)(23,40)(24,27)(25,48)(29,34)(31,44)(33,42)(35,50)(36,39)(37,49)(41,46)(43,45)(47,51);; 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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(51)!(2,3)(4,5)(6,7)(8,9); s1 := Sym(51)!(1,2)(3,4)(5,6)(7,8); s2 := Sym(51)!(12,13)(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)(30,31)(32,35)(33,34)(36,37)(38,41)(39,40)(42,43)(44,47)(45,46)(48,51)(49,50); s3 := Sym(51)!(10,26)(11,20)(12,18)(13,28)(14,16)(15,38)(17,22)(19,32)(21,30)(23,40)(24,27)(25,48)(29,34)(31,44)(33,42)(35,50)(36,39)(37,49)(41,46)(43,45)(47,51); 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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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*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*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 >;