Overview
- Group
- SmallGroup(1008,157)
- Rank
- 4
- Schläfli Type
- {7,2,36}
- Vertices, edges, …
- 7, 7, 36, 36
- Order of s0s1s2s3
- 252
- 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
4-fold
6-fold
9-fold
12-fold
18-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7);; s1 := (1,2)(3,4)(5,6);; s2 := ( 9,10)(11,12)(14,17)(15,16)(18,19)(20,21)(22,25)(23,24)(26,27)(28,29)(30,33)(31,32)(34,35)(36,37)(38,41)(39,40)(42,43);; s3 := ( 8,14)( 9,11)(10,20)(12,22)(13,16)(15,18)(17,28)(19,30)(21,24)(23,26)(25,36)(27,38)(29,32)(31,34)(33,42)(35,39)(37,40)(41,43);; 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,
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(43)!(2,3)(4,5)(6,7); s1 := Sym(43)!(1,2)(3,4)(5,6); s2 := Sym(43)!( 9,10)(11,12)(14,17)(15,16)(18,19)(20,21)(22,25)(23,24)(26,27)(28,29)(30,33)(31,32)(34,35)(36,37)(38,41)(39,40)(42,43); s3 := Sym(43)!( 8,14)( 9,11)(10,20)(12,22)(13,16)(15,18)(17,28)(19,30)(21,24)(23,26)(25,36)(27,38)(29,32)(31,34)(33,42)(35,39)(37,40)(41,43); poly := sub<Sym(43)|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, 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 >;