Overview
- Group
- SmallGroup(1120,302)
- Rank
- 4
- Schläfli Type
- {7,2,40}
- Vertices, edges, …
- 7, 7, 40, 40
- Order of s0s1s2s3
- 280
- 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
5-fold
8-fold
10-fold
20-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)(13,16)(14,18)(15,17)(19,20)(21,26)(22,28)(23,27)(24,30)(25,29)(32,37)(33,36)(34,39)(35,38)(40,41)(42,45)(43,44)(46,47);; s3 := ( 8,14)( 9,11)(10,22)(12,24)(13,17)(15,19)(16,32)(18,34)(20,25)(21,27)(23,29)(26,40)(28,42)(30,35)(31,36)(33,38)(37,46)(39,43)(41,44)(45,47);; 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*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(47)!(2,3)(4,5)(6,7); s1 := Sym(47)!(1,2)(3,4)(5,6); s2 := Sym(47)!( 9,10)(11,12)(13,16)(14,18)(15,17)(19,20)(21,26)(22,28)(23,27)(24,30)(25,29)(32,37)(33,36)(34,39)(35,38)(40,41)(42,45)(43,44)(46,47); s3 := Sym(47)!( 8,14)( 9,11)(10,22)(12,24)(13,17)(15,19)(16,32)(18,34)(20,25)(21,27)(23,29)(26,40)(28,42)(30,35)(31,36)(33,38)(37,46)(39,43)(41,44)(45,47); poly := sub<Sym(47)|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*s2*s3*s2*s3*s2*s3*s2*s3 >;