Overview
- Group
- SmallGroup(1680,990)
- Rank
- 5
- Schläfli Type
- {2,5,2,42}
- Vertices, edges, …
- 2, 5, 5, 42, 42
- Order of s0s1s2s3s4
- 210
- Order of s0s1s2s3s4s3s2s1
- 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
14-fold
21-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (4,5)(6,7);; s2 := (3,4)(5,6);; s3 := (10,11)(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,27)(25,26)(28,29)(30,33)(31,32)(34,35)(36,39)(37,38)(40,41)(42,45)(43,44)(46,49)(47,48);; s4 := ( 8,24)( 9,18)(10,16)(11,26)(12,14)(13,36)(15,20)(17,30)(19,28)(21,38)(22,25)(23,46)(27,32)(29,42)(31,40)(33,48)(34,37)(35,47)(39,44)(41,43)(45,49);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(49)!(1,2); s1 := Sym(49)!(4,5)(6,7); s2 := Sym(49)!(3,4)(5,6); s3 := Sym(49)!(10,11)(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,27)(25,26)(28,29)(30,33)(31,32)(34,35)(36,39)(37,38)(40,41)(42,45)(43,44)(46,49)(47,48); s4 := Sym(49)!( 8,24)( 9,18)(10,16)(11,26)(12,14)(13,36)(15,20)(17,30)(19,28)(21,38)(22,25)(23,46)(27,32)(29,42)(31,40)(33,48)(34,37)(35,47)(39,44)(41,43)(45,49); poly := sub<Sym(49)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;