Overview
- Group
- SmallGroup(1680,966)
- Rank
- 5
- Schläfli Type
- {7,2,10,6}
- Vertices, edges, …
- 7, 7, 10, 30, 6
- 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
3-fold
5-fold
6-fold
10-fold
15-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 := (12,13)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37);; s3 := ( 8,12)( 9,16)(10,20)(11,18)(13,22)(14,26)(15,24)(17,28)(19,32)(21,30)(25,36)(27,34)(31,33)(35,37);; s4 := ( 8,14)( 9,10)(11,15)(12,24)(13,25)(16,18)(17,19)(20,26)(21,27)(22,34)(23,35)(28,30)(29,31)(32,36)(33,37);; 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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(37)!(2,3)(4,5)(6,7); s1 := Sym(37)!(1,2)(3,4)(5,6); s2 := Sym(37)!(12,13)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37); s3 := Sym(37)!( 8,12)( 9,16)(10,20)(11,18)(13,22)(14,26)(15,24)(17,28)(19,32)(21,30)(25,36)(27,34)(31,33)(35,37); s4 := Sym(37)!( 8,14)( 9,10)(11,15)(12,24)(13,25)(16,18)(17,19)(20,26)(21,27)(22,34)(23,35)(28,30)(29,31)(32,36)(33,37); poly := sub<Sym(37)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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 >;